case study questions class 10 maths areas related to circles

• Privacy Policy
• Terms and Conditions

• Web Stories

Monday, October 4, 2021

Class 10 maths case study based questions chapter 12 area related to circles cbse board term 1 with answer key.

Hello students, Welcome to Maths Easy Institute.  

CASE STUDY 1:   

0 comments:

Post a comment.

Please do not enter any spam link in the comment box.

Warning: Do Not Copy!

• Blog Archives

• Best Books for IIT JEE
• Best Colleges Of India
• class 10 Case Study Based questions
• Class 10 Maths MCQ
• Class 11 Maths Case Study Questions
• Class 11 Maths MCQ
• Class 12 Math Case Study questions
• Class 12 Maths MCQ
• JEE MAIN MCQ
• Maths Strategy JEE
• News for Students

Blog Archive

• ►  April (3)
• ►  March (2)
• ►  February (1)
• ►  January (5)
• ►  December (9)
• ►  November (5)
• Case Study Questions Class 10 Maths Chapter 9 Appl...
• Class 10 Maths Case Study Based Questions Chapter ...
• Class 11 Maths MCQ Chapter 5 Complex Numbers CBSE ...
• Class 11 MCQ type Questions Chapter 2 Relations an...
• ►  September (5)
• ►  April (4)
• ►  March (3)
• ►  October (2)
• ►  September (7)
• ►  August (2)
• ►  July (4)

Class 10 Maths Case Study Questions Chapter 12 Areas Related to Circles

• Post author: studyrate
• Post published:
• Post category: class 10th
• Post comments: 0 Comments

Case study Questions in the Class 10 Mathematics Chapter 12  are very important to solve for your exam. Class 10 Maths Chapter 12 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 12  Areas Related to Circles

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Areas Related to Circles Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 12 Areas Related to Circles

Case Study/Passage-Based Questions

Question 1:

Answer: (b) 729 cm2

(ii) Area of rectangle left for car parking is

Answer: (c) 81 cm2

(iii) Radius of semi-circle is

Answer: (a) 6.75 cm

(iv) Area of a semi-circle is

Answer: (d) 71.59 cm2

(v) Find the area of the shaded region

Answer: (b) 666.82 cm2

Question 2:

A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs of some brooch are shown below. Observe them carefully.

Design A:  Brooch A is made with silver wire in the form of a circle with a diameter of 28mm. The wire is used for making 4 diameters which divides the circle into 8 equal parts.

Design B:  Brooch b is made of two colors – Gold and silver. The outer part is made of Gold. The circumference of the silver part is 44mm and the gold part is 3mm wide everywhere.

Refer to Design A

1. The total length of silver wire required is

Answer: b) 200 mm

2. The area of each sector of the brooch is

Answer: c) 77 mm2

Refer to Design B

3. The circumference of outer part (golden) is

a) 48.49 mm

c) 72.50 mm

d) 62.86 mm

Answer: d) 62.86 mm

4. The difference of areas of golden and silver parts is

a) 18  π

b) 44  π

c) 51  π

d) 64  π

Answer: c) 51 π

5. A boy is playing with brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 80 mm?

Answer: c) 4

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 12 Areas Related to Circles with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Areas Related to Circles Case Study and Passage-Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

You Might Also Like

Extra questions of class 10 social science geography chapter 2 forests and wildlife resources pdf download, assertion reason questions class 10 science chapter 12 electricity, case study questions class 10 civics – outcomes of democracy, leave a reply cancel reply.

Save my name, email, and website in this browser for the next time I comment.

• Bihar Board

SRM University

नए भारत का नया उत्तर प्रदेश.

• Bihar Board Result 2024
• UP Board Result 2024
• CBSE Board Result 2024
• MP Board Result 2024
• Rajasthan Board Result 2024
• Shiv Khera Special
• Education News
• Web Stories
• Current Affairs
• School & Boards
• College Admission
• Govt Jobs Alert & Prep
• GK & Aptitude
• CBSE Class 10 Study Material

CBSE Class 10 Maths Case Study Questions for Chapter 10 - Circles (Published By CBSE)

Check cbse class 10 maths case study questions for chapter 10 - circles. these questions have been published by the board for class 10 mathematics..

CBSE: Case study questions for CBSE Class 10 Maths Chapter 10 - Circles are provided here which students can practice to get familiarised with the new format of questions. These questions have been published by CBSE itself. Answers to all the questions have been provided for the convenience of students. Case study questions are helpful for the preparation of the Class 10 Maths Exam 2021-2022.

Case Study Questions for Class 10 Maths Chapter 10 - Circles

CASE STUDY 1:

A Ferris wheel (or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger-carrying components (commonly referred to as passenger cars, cabins, tubs, capsules, gondolas, or pods) attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.

After taking a ride in Ferris wheel, Aarti came out from the crowd and was observing her friends who were enjoying the ride . She was curious about the different angles and measures that the wheel will form. She forms the figure as given below.

1. In the given figure find ∠ROQ

Answer: c) 150

2. Find ∠RQP

Answer: a) 75

3. Find ∠RSQ

Answer: b) 75

4. Find ∠ORP

Answer: a) 90

CASE STUDY 2:

Varun has been selected by his School to design logo for Sports Day T-shirts for students and staff . The logo design is as given in the figure and he is working on the fonts and different colours according to the theme. In given figure, a circle with centre O is inscribed in a ΔABC, such that it touches the sides AB, BC and CA at points D, E and F respectively. The lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm respectively.

1. Find the length of AD

Answer: a) 7

2. Find the Length of BE

Answer: b) 5

3. Find the length of CF

Answer: d) 3

4. If radius of the circle is 4cm, Find the area of ∆OAB

Answer: c) 24

5. Find area of ∆ABC

Answer: b) 60

Also Check:

Tips to Solve Case Study Based Questions Accurately

Get here latest School , CBSE and Govt Jobs notification in English and Hindi for Sarkari Naukari and Sarkari Result . Download the Jagran Josh Sarkari Naukri App . Check  Board Result 2024  for Class 10 and Class 12 like  CBSE Board Result ,  UP Board Result ,  Bihar Board Result ,  MP Board Result ,  Rajasthan Board Result  and Other States Boards.

• AP TET Results 2024
• SSC GD Answer Key 2024
• CBSE Class 12 Bio Practice Papers 2024
• CBSE Class 12 Biology MCQ
• CBSE Class 12 Biology Important Diagrams
• GPSC DYSO Result 2024
• JKSSB SI Answer Key 2024
• Bihar Sakshamta Pariskha Answer Key 2024
• SEBI Grade A Recruitment 2024
• MPNRC Result 2024

Trending Categories

• CBSE Study Material
• CBSE Class 10

Latest Education News

Only 2% With Vision Like An Eagle Can Spot Three Eggs In 12 Seconds!

Bihar Board Class 12th Result 2024 LIVE: नया अपडेट! बिहार दिवस के दिन आ सकता है BSEB इंटर का रिजल्ट, देखें लेटेस्ट अपडेट्स

Picture Puzzle IQ Test: Find the mistake in the kids playing picture in 4 seconds!

Spot The Mistake Hidden In This Garden Scene Within 23 Seconds. Only 5% Won!

IPL 2024 MI Players: मुंबई इंडियन्स के खिलाड़ियों की पूरी लिस्ट यहां देखें     

GK Quiz on Baseball: A Baseball Trivia Quiz to Test Your Mettle

Spot 3 differences between the girl jumping on cliff image in 12 seconds.

Karnataka government bans Hookah: What could be the rationale? Understanding the row between state government and hookah cafes

APSC CCE Answer Key 2024 OUT at apsc.nic.in, Submit Objection

Important Days in March 2024: National and International Dates List

Chaitra Navratri 2024: Date, Ghatsthapna Timings, Puja Muhurat, Significance & More

Optical Illusion Challenge: Find the hidden potato among hamsters in 7 seconds!

List of Average IQ in Every State of the USA

NIFT Result 2024 Releases Soon at exams.nta.ac.in, Check Past Year Trends Here

SSC GD Answer Key 2024 Live: Constable answer sheet soon at ssc.gov.in

CBSE Accountancy Syllabus for Class 12 2024: Download Revised PDF with Important Resources

Most Five Wicket Hauls in IPL History: List of Bowlers With Five Wickets in Single Innings

ISO की ओर से कितने प्रकार के जारी किए जाते हैं प्रमाणपत्र, पढ़ें

TS Inter 2nd Year Geography Model Question Paper 2024: Download FREE PDF

Highest Successful Run Chases in IPL History (2008-2024)

myCBSEguide

• Mathematics
• Case Study Class 10...

Case Study Class 10 Maths Questions

Table of Contents

myCBSEguide App

Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

• Real Numbers Case Study Question
• Polynomials Case Study Question
• Pair of Linear Equations in Two Variables Case Study Question
• Quadratic Equations Case Study Question
• Arithmetic Progressions Case Study Question
• Triangles Case Study Question
• Coordinate Geometry Case Study Question
• Introduction to Trigonometry Case Study Question
• Some Applications of Trigonometry Case Study Question
• Circles Case Study Question
• Area Related to Circles Case Study Question
• Surface Areas and Volumes Case Study Question
• Statistics Case Study Question
• Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

• Find the production in the 1 st year.
• Find the production in the 12 th year.
• Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

• Find the distance between Lucknow (L) to Bhuj(B).
• If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
• Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

• Find the distance PA.
• Find the distance PB
• Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

• What is the length of the line segment joining points B and F?
• The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
• What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

• If the first circular row has 30 seats, how many seats will be there in the 10th row?
• For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
• If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

• Draw a neat labelled figure to show the above situation diagrammatically.

• What is the speed of the plane in km/hr.

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

Related Posts

• CBSE Class 10 Maths Sample Paper 2020-21
• Class 12 Maths Case Study Questions
• CBSE Reduced Syllabus Class 10 (2020-21)
• Class 10 Maths Basic Sample Paper 2024
• How to Revise CBSE Class 10 Maths in 3 Days
• CBSE Practice Papers 2023
• Class 10 Maths Sample Papers 2024
• Competency Based Learning in CBSE Schools

Leave a Comment

Save my name, email, and website in this browser for the next time I comment.

• Class 6 Maths
• Class 6 Science
• Class 6 Social Science
• Class 6 English
• Class 7 Maths
• Class 7 Science
• Class 7 Social Science
• Class 7 English
• Class 8 Maths
• Class 8 Science
• Class 8 Social Science
• Class 8 English
• Class 9 Maths
• Class 9 Science
• Class 9 Social Science
• Class 9 English
• Class 10 Maths
• Class 10 Science
• Class 10 Social Science
• Class 10 English
• Class 11 Maths
• Class 11 Computer Science (Python)
• Class 11 English
• Class 12 Maths
• Class 12 English
• Class 12 Economics
• Class 12 Accountancy
• Class 12 Physics
• Class 12 Chemistry
• Class 12 Biology
• Class 12 Computer Science (Python)
• Class 12 Physical Education
• GST and Accounting Course
• Excel Course
• Tally Course
• Finance and CMA Data Course
• Payroll Course

Interesting

• Learn English
• Learn Excel
• Learn Tally
• Learn GST (Goods and Services Tax)
• Learn Accounting and Finance
• GST Tax Invoice Format
• Accounts Tax Practical
• Tally Ledger List
• GSTR 2A - JSON to Excel

Are you in school ? Do you love Teachoo?

We would love to talk to you! Please fill this form so that we can contact you

You are learning...

Chapter 11 Class 10 Areas related to Circles

Click on any of the links below to start learning from Teachoo ...

Updated for new NCERT - 2023-2024 Boards.

NCERT Solutions of all exercise questions and examples of Chapter 11 Class 10 Areas related to Circle. Answers to all questions are available with video free at teachoo.

In this chapter, we will

• Revise our concepts about Area and Perimeter of Circle , and do some questions
• Then, we will see what arc , sector and segment of a circle is
• We will learn the formula for length of an arc
• and Area of sector
• Then, using Area of sector and Area of triangle formulas, we find Area of Segment
• We do some questions where different figures are combined, and we need to find their area and perimeter

Click on an exercise link below to learn from the NCERT Book way.

Or you can also learn from Teachoo way, click on any concept below Concept Wise to get started.

In concept wise, the chapter is divided into concepts. First the concept is taught, and then we solve the questions related to the concept. All questions are ordered easy to difficult. That means, easiest question is in the beginning and the more difficult question is at the end.

Click on any link below to start studying the chapter.

Serial order wise

Concept wise.

What's in it?

Hi, it looks like you're using AdBlock :(

Please login to view more pages. it's free :), solve all your doubts with teachoo black.

Study Material

Home > Class 10 Maths Subject-wise Material

Class 10 Maths Chapter 12 Areas Related to Circle

CBSE Class 10 Mathematics "Areas Related to Circles" chapter is important to creating a solid geometric foundation, getting students ready for future phases, and using mathematical concepts in everyday situations. It is suggested that students work through a range of problem-solving exercises to solidify their comprehension of the subject. 

Given that this concept is covered in the CBSE Class 10 Mathematics syllabus, examination success depends on learning it. Area of circle questions are frequently found in board exams and other competitive tests. This topic combines comprehension of lengths, angles, and circles to give a thorough grasp of how these ideas relate to one another. Students need to do this since it improves their ability to solve problems.

On this page, students may find reliable study materials like class 10 maths chapter 11 notes, learning activities, DoE worksheets, and other support materials from Educart.

CBSE Class X Areas Related to Circles Notes

Class 10 Areas Related to Circles Chapter 11  notes cover all the main concepts like tangents, chords, secant, and many others. The downloadable notes PDFs for Areas Related to Areas Related to Circles are provided below in detailed and easy-to-understand language.

<red> ➜   <red>Areas Related to Circles Class 10 Notes

📈 Trending: Class 10 CBSE Admit Card 2024

📺 Recommended: Important Questions PDFs for Class 10

📚 Don't Miss: CBSE Class 10 Sample Question Papers

CBSE Class X Areas Related to Circles DoE Worksheet

Students can attempt the class 10 maths Areas Related to Circles chapter 11 worksheet to prepare themselves as per the exam pattern. Below we have provided the links to downloadable PDFs of DoE Worksheets for class 10 Mathematics to practice more questions. 

<red> ➜   <red>Worksheet 49

<red> ➜  <red>worksheet 50, <red> ➜   <red>worksheet 51, <red> ➜   <red>worksheet 52, <red> ➜  <red>worksheet 53, cbse class 10 areas related to circle experiential activities.

In the table below, we have provided the links to downloadable PDFs of Experiential Learning Activity for class 10 Mathematics to help students implement their acquired knowledge in the real world.

<red> ➜   <red>Area Related to Circle Experiential Activities

Cbse class x areas related to circles formulas.

Below we have provided the links for Areas Related to Circles class 10 math formulas to help students solve complex questions and understand the concepts easily. 

<red> ➜   <red>Class 10 Mathematics Formulas(View)

Cbse class x areas related to circles mind-maps.

Below we have provided the links to downloadable PDFs of Mind maps for Areas Related to Circles class 10 Mathematics to help students implement their acquired knowledge in the real world.

<red> ➜   <red>Class 10 Mathematics Mind-maps

Cbse class x areas related to areas related to circles important questions.

Below we have provided Class 10 Mathematics Important Questions that cover questions from the NCERT textbook. 

<red> ➜   <red>Class 10 Mathematics Important Questions(View)

Cbse class x areas related to areas related to circles question bank.

Below we have provided Class 10 Mathematics Question Banks that cover every typology question with detailed explanations from various resources in one place.

<red> ➜   <red>Areas Related to Circles CBSE Question Bank

<red> ➜   <red>areas related to circles kendriya vidyalaya question bank, cbse class x areas related to areas related to circles support material.

Below we have provided Class 10 Mathematics Support Material that covers Case-study-based questions from the various concepts explained in NCERT chapters. 

<red> ➜   <red>Areas Related to Circles Practice Test

<red> ➜   <red>areas related to circles support material    , why download these chapter-wise pdfs.

For courses like Mathematics, including areas related to circle class 10 Ch 11 Maths, downloading chapter-specific PDFs can have the following benefits:

• Chapter-specific studying using PDFs is arranged and structured. It is simpler for students to efficiently organize their study time when they can concentrate on particular topics or chapters.
• Collaborative learning is encouraged when students discuss the PDFs with their instructors or fellow students. This is particularly helpful while studying in groups or looking for help from others.
• PDFs may be accessible offline after they have been downloaded, enabling students to continue their studies even in the absence of an internet connection. Students who only sometimes have regular access to the web will find this very useful.
• PDFs are lightweight and compatible with many different devices. This mobility encourages flexibility in learning plans by allowing students to study Chapter 11 on Areas Related to Circles whenever and wherever they want.
• Chapter-wise revision and review are made possible by PDFs. Before tests, students may review particular chapters or subjects to assist in solidifying their learning.

How Can This Chapter-wise Material Help Students?

Students can use chapter-by-chapter for chapter 11 math class 10 resources as a fast reference. They don't have to look through the entire textbook to find a topic or formula they need to review—they can find it quickly in the pertinent chapter. Students can concentrate on one chapter at a time while studying at their own speed. They may spend more time on difficult subjects and get through concepts more rapidly when they study at their speed. After downloading chapter notes, DoE worksheets, question banks, and many other study materials, students can prepare for the chapter effectively.

• Students can better organize their study time using chapter-wise Ch 10 math class 10 circle notes. To ensure that they methodically finish the full syllabus, they might set out particular time intervals for each chapter.
• Mind maps are great tools for fast revision since they provide information clearly and straightforwardly. Before tests, students can effectively go through the entire chapter again.
• Students who practice with a question bank also get better at managing their time. It gets students ready for test time limits since they have to answer a range of questions in a limited amount of time.
• Worksheets organized by chapter may be an invaluable resource for preparing for exams. They address a variety of circle-related issues, some of which may resemble test questions for pupils. This enhances their exam-taking abilities and gets them ready for a variety of question types.
• Through practical lessons that go beyond typical textbook learning, these exercises provide students with a better grasp of mathematical ideas. 
• It is necessary to comprehend and practice these formulae to solve circle-related difficulties. Applying and practicing these ideas regularly can help you finish the chapter quickly and do well on tests. 
• Understanding the geometric meaning of these formulae also helps with problem-solving and establishes a solid basis for future mathematical research.

Chapter-by-chapter, class 10 CBSE Math Area Related to Circles study materials by Educart are excellent tools that help students study in a more structured and efficient manner, particularly when they are getting ready for an exam. Students usually choose to review particular topics to get ready for a test. Chapter-by-chapter resources provide for focused review, allowing students to focus on Areas in which they are less confident. All you need to download these PDFs is a single click and user authentication.

Class 10 Subject-wise Material

Class 10 important questions, ncert books for class 10.

Buy Latest Books

Teacher's Corner

To Download PDF

Please verify your Whatsapp number first, so you can download unlimited pdfs for free

Please type a valid 10 digit whatsapp number

OTP sent, check your whatsapp

Your OTP is incorrect, Please enter valid OTP

• Mathematics (Standard)
• Mathematics (Basic)
• Social Science
• Computer Application
• Information Technology
• English Core
• Mathematics
• Accountancy
• Business Studies
• Political Science
• Science (Hindi )
• Maths (Hindi)
• Social Science (Hindi )
• English (Hindi)
• Applied Maths
• Physical Education
• 40 Sample Papers
• English Language
• English Literature
• History & Civics
• 10 Year Solved Papers
• Class 10 Science
• Class 10 Maths
• Class 10 English
• Class 12 Physics
• Class 12 Chemistry
• Class 12 Biology
• Class 12 Maths
• Class 12 English
• Math Standard
• Computer Applications
• Class 12 PCM Bundle
• Entrance Exam
• K-8 Raspberry Solutions
• K-8 Kiwi Solutions

CBSE Case Study Questions for Class 10 Maths Area Related to Circles Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Area Related to Circles  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

MCQ Set 1 -

Mcq set 2 -, checkout our case study questions for other chapters.

• Chapter 10: Circles Case Study Questions
• Chapter 11: Construction Case Study Questions
• Chapter 13: Surface Area and Volumes Case Study Questions
• Chapter 14: Statistics Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

Contact Form

Privacy Policy

• NCERT Solutions
• NCERT Solutions for Class 10
• NCERT Solutions for Class 10 Maths
• Chapter 12: Areas Related To Circles

NCERT Solutions For Class 10 Maths Chapter 12 Areas Related to Circles

Ncert solutions for class 10 maths chapter 12 – cbse free pdf download.

* According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 11.

NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles are important study resources needed for the students in Class 10. These NCERT Solutions for Class 10 Maths help the students understand the types of questions that will be asked in the CBSE Class 10 Maths board exams. Moreover, providing solutions to all areas related to circles help students in preparing for the CBSE exams in an effective way.

Download Exclusively Curated Chapter Notes for Class 10 Maths Chapter – 12 Areas Related to Circles

Download most important questions for class 10 maths chapter – 12 areas related to circles.

The NCERT Solutions for Class 10 Maths , available at BYJUS, will help students ace their board exams by preparing for them well in advance. Get free Maths NCERT Solutions for Class 10 of this chapter and clear all conceptual doubts. To assist the students of Class 10 in being better prepared for their board exams, the experts have formulated these NCERT Solutions based on the latest update on the CBSE syllabus for 2023-24.

• Chapter 1 Real Numbers
• Chapter 2 Polynomials
• Chapter 3 Pair of Linear Equations in Two Variables
• Chapter 4 Quadratic Equations
• Chapter 5 Arithmetic Progressions
• Chapter 6 Triangles
• Chapter 7 Coordinate Geometry
• Chapter 8 Introduction to Trigonometry
• Chapter 9 Some Applications of Trigonometry
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Areas Related to Circles
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability

NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles

carouselExampleControls112

Previous Next

Access answers of Maths NCERT Class 10 Chapter 12 – Areas Related to Circles

Class 10 maths chapter 12 exercise: 12.1 (page no: 230).

Exercise: 12.1 (Page No: 230)

1. The radii of the two circles are 19 cm and 9 cm, respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.

The radius of the 1 st circle = 19 cm (given)

∴ circumference of the 1 st circle = 2π×19 = 38π cm

The radius of the 2 nd circle = 9 cm (given)

∴ circumference of the 2 nd circle = 2π×9 = 18π cm

The sum of the circumference of two circles = 38π+18π = 56π cm

Now, let the radius of the 3 rd circle = R

∴ the circumference of the 3 rd circle = 2πR

It is given that sum of the circumference of two circles = circumference of the 3 rd circle

Hence, 56π = 2πR

Or, R = 28 cm.

2. The radii of the two circles are 8 cm and 6 cm, respectively. Find the radius of the circle having an area equal to the sum of the areas of the two circles.

The radius of 1 st circle = 8 cm (given)

∴ area of 1 st circle = π(8) 2 = 64π

The radius of 2 nd circle = 6 cm (given)

∴ area of 2 nd circle = π(6) 2 = 36π

The sum of 1 st and 2 nd circle will be = 64π+36π = 100π

Now, assume that the radius of 3 rd circle = R

∴ area of the circle 3 rd circle = πR 2

It is given that the area of the circle 3 rd circle = Area of 1 st circle + Area of 2 nd circle

Or, πR 2 = 100πcm 2

R 2 = 100cm 2

So, R = 10cm

3. Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing the Gold score is 21 cm, and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

The radius of 1 st circle, r 1 = 21/2 cm (as diameter D is given as 21 cm)

So, area of gold region = π r 1 2 = π(10.5) 2 = 346.5 cm 2

Now, it is given that each of the other bands is 10.5 cm wide,

So, the radius of 2 nd circle, r 2 = 10.5cm+10.5cm = 21 cm

∴ area of red region = Area of 2 nd circle − Area of gold region = (πr 2 2 −346.5) cm 2

= (π(21) 2 − 346.5) cm 2

= 1386 − 346.5

= 1039.5 cm 2

The radius of 3 rd circle, r 3 = 21 cm+10.5 cm = 31.5 cm

The radius of 4 th circle, r 4 = 31.5 cm+10.5 cm = 42 cm

The Radius of 5 th circle, r 5 = 42 cm+10.5 cm = 52.5 cm

For the area of n th region,

A = Area of circle n – Area of the circle (n-1)

∴ area of the blue region (n=3) = Area of the third circle – Area of the second circle

= π(31.5) 2 – 1386 cm 2

= 3118.5 – 1386 cm 2

= 1732.5 cm 2

∴ area of the black region (n=4) = Area of the fourth circle – Area of the third circle

= π(42) 2 – 1386 cm 2

= 5544 – 3118.5 cm 2

= 2425.5 cm 2

∴ area of the white region (n=5) = Area of the fifth circle – Area of the fourth circle

= π(52.5) 2 – 5544 cm 2

= 8662.5 – 5544 cm 2

= 3118.5 cm 2

4. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

The radius of car’s wheel = 80/2 = 40 cm (as D = 80 cm)

So, the circumference of wheels = 2πr = 80 π cm

Now, in one revolution, the distance covered = circumference of the wheel = 80 π cm

It is given that the distance covered by the car in 1 hr = 66km

Converting km into cm, we get,

Distance covered by the car in 1hr = (66×10 5 ) cm

In 10 minutes, the distance covered will be = (66×10 5 ×10)/60 = 1100000 cm/s

∴ distance covered by car = 11×10 5 cm

Now, the no. of revolutions of the wheels = (Distance covered by the car/Circumference of the wheels)

=( 11×10 5 )/80 π = 4375.

5. Tick the correct solution in the following and justify your choice. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

(A) 2 units

(B) π units

(C) 4 units

(D) 7 units

Since the perimeter of the circle = area of the circle,

So, option (A) is correct, i.e., the radius of the circle is 2 units.

Exercise: 12.2 (Page No: 230)

1. Find the area of a sector of a circle with a radius 6 cm if the angle of the sector is 60°.

It is given that the angle of the sector is 60°

We know that the area of sector = (θ/360°)×πr 2

∴ area of the sector with angle 60° = (60°/360°)×πr 2 cm 2

= (36/6)π cm 2

= 6×22/7 cm 2 = 132/7 cm 2

2. Find the area of a quadrant of a circle whose circumference is 22 cm.

Circumference of the circle, C = 22 cm (given)

It should be noted that a quadrant of a circle is a sector which is making an angle of 90°.

Let the radius of the circle = r

As C = 2πr = 22,

R = 22/2π cm = 7/2 cm

∴ area of the quadrant = (θ/360°) × πr 2

Here, θ = 90°

So, A = (90°/360°) × π r 2 cm 2

= (49/16) π cm 2

= 77/8 cm 2 = 9.6 cm 2

3. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Length of minute hand = radius of the clock (circle)

∴ Radius (r) of the circle = 14 cm (given)

Angle swept by minute hand in 60 minutes = 360°

So, the angle swept by the minute hand in 5 minutes = 360° × 5/60 = 30°

Area of a sector = (θ/360°) × πr 2

Now, the area of the sector making an angle of 30° = (30°/360°) × πr 2 cm 2

= (1/12) × π14 2

= (49/3)×(22/7) cm 2

= 154/3 cm 2

4. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:

(i) minor segment

(ii) major sector. (Use π = 3.14)

Here, AB is the chord which is subtending an angle 90° at the centre O.

It is given that the radius (r) of the circle = 10 cm

(i) Area of minor sector = (90/360°)×πr 2

= (¼)×(22/7)×10 2

Or, the Area of the minor sector = 78.5 cm 2

Also, the area of ΔAOB = ½×OB×OA

Here, OB and OA are the radii of the circle, i.e., = 10 cm

So, the area of ΔAOB = ½×10×10

Now, area of minor segment = area of the minor sector – the area of ΔAOB

= 78.5 – 50

= 28.5 cm 2

(ii) Area of major sector = Area of the circle – Area of he minor sector

= (3.14×10 2 )-78.5

= 235.5 cm 2

5. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:

(i) the length of the arc

(ii) area of the sector formed by the arc

(iii) area of the segment formed by the corresponding chord

Radius = 21 cm

(i) Length of an arc = θ/360°×Circumference(2πr)

∴ Length of an arc AB = (60°/360°)×2×(22/7)×21

= (1/6)×2×(22/7)×21

Or Arc AB Length = 22cm

(ii) It is given that the angle subtended by the arc = 60°

So, the area of the sector making an angle of 60° = (60°/360°)×π r 2 cm 2

= 441/6×22/7 cm 2

Or, the area of the sector formed by the arc APB is 231 cm 2

(iii) Area of segment APB = Area of sector OAPB – Area of ΔOAB

Since the two arms of the triangle are the radii of the circle and thus are equal, and one angle is 60°, ΔOAB is an equilateral triangle. So, its area will be √3/4×a 2 sq. Units.

The area of segment APB = 231-(√3/4)×(OA) 2

= 231-(√3/4)×21 2

Or, the area of segment APB = [231-(441×√3)/4] cm 2

6. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)

Radius = 15 cm

Area of sector OAPB = (60°/360°)×πr 2 cm 2

= 225/6 πcm 2

Now, ΔAOB is equilateral as two sides are the radii of the circle and hence equal and one angle is 60°

So, Area of ΔAOB = (√3/4) ×a 2

Or, (√3/4) ×15 2

∴ Area of ΔAOB = 97.31 cm 2

Now, the area of minor segment APB = Area of OAPB – Area of ΔAOB

Or, the area of minor segment APB = ((225/6)π – 97.31) cm 2 = 20.43 cm 2

Area of major segment = Area of the circle – Area of the segment APB

Or, area of major segment = (π×15 2 ) – 20.4 = 686.06 cm 2

7. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73)

Radius, r = 12 cm

Now, draw a perpendicular OD on chord AB, and it will bisect chord AB.

So, AD = DB

Now, the area of the minor sector = (θ/360°)×πr 2

= (120/360)×(22/7)×12 2

= 150.72 cm 2

Consider the ΔAOB,

∠ OAB = 180°-(90°+60°) = 30°

Now, cos 30° = AD/OA

√3/2 = AD/12

Or, AD = 6√3 cm

We know OD bisects AB. So,

AB = 2×AD = 12√3 cm

Now, sin 30° = OD/OA

Or, ½ = OD/12

∴ OD = 6 cm

So, the area of ΔAOB = ½ × base × height

Here, base = AB = 12√3 and

Height = OD = 6

So, area of ΔAOB = ½×12√3×6 = 36√3 cm = 62.28 cm 2

∴ area of the corresponding Minor segment = Area of the Minor sector – Area of ΔAOB

= 150.72 cm 2 – 62.28 cm 2 = 88.44 cm 2

8. A horse is tied to a peg at one corner of a square-shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). Find

(i) the area of that part of the field in which the horse can graze.

(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)

As the horse is tied at one end of a square field, it will graze only a quarter (i.e. sector with θ = 90°) of the field with a radius 5 m.

Here, the length of the rope will be the radius of the circle, i.e. r = 5 m

It is also known that the side of the square field = 15 m

(i) Area of circle = πr 2 = 22/7 × 5 2 = 78.5 m 2

Now, the area of the part of the field where the horse can graze = ¼ (the area of the circle) = 78.5/4 = 19.625 m 2

(ii) If the rope is increased to 10 m,

Area of circle will be = πr 2 =22/7×10 2 = 314 m 2

Now, the area of the part of the field where the horse can graze = ¼ (the area of the circle)

= 314/4 = 78.5 m 2

∴ increase in the grazing area = 78.5 m 2 – 19.625 m 2 = 58.875 m 2

9. A brooch is made with silver wire in the form of a circle with a diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors, as shown in Fig. 12.12. Find:

(i) the total length of the silver wire required.

(ii) the area of each sector of the brooch.

Diameter (D) = 35 mm

Total number of diameters to be considered= 5

Now, the total length of 5 diameters that would be required = 35×5 = 175

Circumference of the circle = 2πr

Or, C = πD = 22/7×35 = 110

Area of the circle = πr 2

Or, A = (22/7)×(35/2) 2 = 1925/2 mm 2

(i) Total length of silver wire required = Circumference of the circle + Length of 5 diameter

= 110+175 = 285 mm

(ii) Total Number of sectors in the brooch = 10

So, the area of each sector = total area of the circle/number of sectors

∴ Area of each sector = (1925/2)×1/10 = 385/4 mm 2

10. An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming the umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

The radius (r) of the umbrella when flat = 45 cm

So, the area of the circle (A) = πr 2 = (22/7)×(45) 2 =6364.29 cm 2

Total number of ribs (n) = 8

∴ The area between the two consecutive ribs of the umbrella = A/n

6364.29/8 cm 2

Or, The area between the two consecutive ribs of the umbrella = 795.5 cm 2

11. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.

Radius (r) = 25 cm

Sector angle (θ) = 115°

Since there are 2 blades,

The total area of the sector made by wiper = 2×(θ/360°)×π r 2

= 2×(115/360)×(22/7)×25 2

= 2×158125/252 cm 2

= 158125/126 = 1254.96 cm 2

12. To warn ships of underwater rocks, a lighthouse spreads a red-coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned.

(Use π = 3.14)

Let O bet the position of the lighthouse.

Here, the radius will be the distance over which light spreads.

Given radius (r) = 16.5 km

Sector angle (θ) = 80°

Now, the total area of the sea over which the ships are warned = Area made by the sector

Or, Area of sector = (θ/360°)×πr 2

= (80°/360°)×πr 2 km 2

= 189.97 km 2

13. A round table cover has six equal designs, as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm 2 . (Use √3 = 1.7)

Total number of equal designs = 6

AOB= 360°/6 = 60°

The radius of the cover = 28 cm

Cost of making design = ₹ 0.35 per cm 2

Since the two arms of the triangle are the radii of the circle and thus are equal, and one angle is 60°, ΔAOB is an equilateral triangle. So, its area will be (√3/4)×a 2 sq. units

Here, a = OA

∴ Area of equilateral ΔAOB = (√3/4)×28 2 = 333.2 cm 2

Area of sector ACB = (60°/360°)×πr 2 cm 2

= 410.66 cm 2

So, the area of a single design = the area of sector ACB – the area of ΔAOB

= 410.66 cm 2 – 333.2 cm 2 = 77.46 cm 2

∴ area of 6 designs = 6×77.46 cm 2 = 464.76 cm 2

So, total cost of making design = 464.76 cm 2 ×Rs.0.35 per cm 2

= Rs. 162.66

14. Tick the correct solution in the following:

The area of a sector of angle p (in degrees) of a circle with radius R is

(A) p/180 × 2πR

(B) p/180 × π R 2

(C) p/360 × 2πR

(D) p/720 × 2πR 2

The area of a sector = (θ/360°)×πr 2

Given, θ = p

So, the area of sector = p/360×πR 2

Multiplying and dividing by 2 simultaneously,

= (p/360)×2/2×πR 2

= (2p/720)×2πR 2

So, option (D) is correct.

Exercise: 12.3 (Page No: 234)

1. Find the area of the shaded region in Fig. 12.19, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.

Here, P is in the semi-circle, and so,

So, it can be concluded that QR is the hypotenuse of the circle and is equal to the diameter of the circle.

Using the Pythagorean theorem,

QR 2 = PR 2 +PQ 2

Or, QR 2 = 7 2 +24 2

QR= 25 cm = Diameter

Hence, the radius of the circle = 25/2 cm

Now, the area of the semicircle = (πR 2 )/2

= (22/7)×(25/2)×(25/2)/2 cm 2

= 13750/56 cm 2 = 245.54 cm 2

Also, the area of the ΔPQR = ½×PR×PQ

=(½)×7×24 cm 2

Hence, the area of the shaded region = 245.54 cm 2 -84 cm 2

= 161.54 cm 2

2. Find the area of the shaded region in Fig. 12.20, if the radii of the two concentric circles with centre O are 7 cm and 14 cm, respectively and AOC = 40°.

Angle made by sector = 40°,

Radius the inner circle = r = 7 cm, and

Radius of the outer circle = R = 14 cm

Area of the sector = (θ/360°)×πr 2

So, Area of OAC = (40°/360°)×πr 2 cm 2

= 68.44 cm 2

Area of the sector OBD = (40°/360°)×πr 2 cm 2

= (1/9)×(22/7)×7 2 = 17.11 cm 2

Now, the area of the shaded region ABDC = Area of OAC – Area of the OBD

= 68.44 cm 2 – 17.11 cm 2 = 51.33 cm 2

3. Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Side of the square ABCD (as given) = 14 cm

So, the Area of ABCD = a 2

= 14×14 cm 2 = 196 cm 2

We know that the side of the square = diameter of the circle = 14 cm

So, the side of the square = diameter of the semicircle = 14 cm

∴ the radius of the semicircle = 7 cm

= (22/7×7×7)/2 cm 2 

∴ he area of two semicircles = 2×77 cm 2 = 154 cm 2

Hence, the area of the shaded region = Area of the Square – Area of two semicircles

= 196 cm 2 -154 cm 2

4. Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as the centre.

It is given that OAB is an equilateral triangle having each angle as 60°

The area of the sector is common in both.

The radius of the circle = 6 cm

Side of the triangle = 12 cm

Area of the equilateral triangle = (√3/4) (OA) 2 = (√3/4)×12 2 = 36√3 cm 2

Area of the circle = πR 2 = (22/7)×6 2 = 792/7 cm 2

Area of the sector making angle 60° = (60°/360°) ×πr 2 cm 2

= (1/6)×(22/7)× 6 2 cm 2 = 132/7 cm 2

Area of the shaded region = Area of the equilateral triangle + Area of the circle – Area of the sector

= 36√3 cm 2 +792/7 cm 2 -132/7 cm 2

= (36√3+660/7) cm 2

5. From each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig. 12.23. Find the area of the remaining portion of the square.

Side of the square = 4 cm

The radius of the circle = 1 cm

Four quadrants of a circle are cut from the corner, and one circle of radius are cut from the middle.

Area of the square = (side) 2 = 4 2 = 16 cm 2

Area of the quadrant = (πR 2 )/4 cm 2 = (22/7)×(1 2 )/4 = 11/14 cm 2

∴ Total area of the 4 quadrants = 4 ×(11/14) cm 2 = 22/7 cm 2

Area of the circle = πR 2 cm 2 = (22/7×1 2 ) = 22/7 cm 2

Area of the shaded region = Area of the square – (Area of the 4 quadrants + Area of the circle)

= 16 cm 2 -(22/7) cm 2  – (22/7) cm 2

= 68/7 cm 2

6. In a circular table cover of radius 32 cm, a design is formed, leaving an equilateral triangle ABC in the middle, as shown in Fig. 12.24. Find the area of the design.

The radius of the circle = 32 cm

Draw a median AD of the triangle passing through the centre of the circle.

⇒ BD = AB/2

Since, AD is the median of the triangle

∴ AO = Radius of the circle = (2/3) AD

⇒ (2/3)AD = 32 cm

⇒ AD = 48 cm

By Pythagoras’ theorem,

AB 2 = AD 2 +BD 2

⇒ AB 2 = 48 2 +(AB/2) 2

⇒ AB 2 = 2304+AB 2 /4

⇒ 3/4 (AB 2 )= 2304

⇒ AB 2 = 3072

⇒ AB= 32√3 cm

Area of ΔADB = √3/4 ×(32√3) 2 cm 2 = 768√3 cm 2

Area of the circle = πR 2 = (22/7)×32×32 = 22528/7 cm 2

Area of the design = Area of the circle – Area of ΔADB

= (22528/7 – 768√3) cm 2

7. In Fig. 12.25, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.

Side of square = 14 cm

Four quadrants are included in the four sides of the square.

∴ radius of the circles = 14/2 cm = 7 cm

Area of the square ABCD = 14 2 = 196 cm 2

Area of the quadrant = (πR 2 )/4 cm 2 = (22/7) ×7 2 /4 cm 2

= 77/2 cm 2

Total area of the quadrant = 4×77/2 cm 2 = 154cm 2

Area of the shaded region = Area of the square ABCD – Area of the quadrant

= 196 cm 2 – 154 cm 2

8. Fig. 12.26 depicts a racing track whose left and right ends are semicircular.

The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find

(i) the distance around the track along its inner edge

(ii) the area of the track.

Width of the track = 10 m

Distance between two parallel lines = 60 m

Length of parallel tracks = 106 m

DE = CF = 60 m

The radius of the inner semicircle, r = OD = O’C

= 60/2 m = 30 m

The radius of the outer semicircle, R = OA = O’B

= 30+10 m = 40 m

Also, AB = CD = EF = GH = 106 m

Distance around the track along its inner edge = CD+EF+2×(Circumference of inner semicircle)

= 106+106+(2×πr) m = 212+(2×22/7×30) m

= 212+1320/7 m = 2804/7 m

Area of the track = Area of ABCD + Area EFGH + 2 × (area of outer semicircle) – 2 × (area of inner semicircle)

= (AB×CD)+(EF×GH)+2×(πr 2 /2) -2×(πR 2 /2) m 2

= (106×10)+(106×10)+2×π/2(r 2 -R 2 ) m 2

= 2120+22/7×70×10 m 2

9. In Fig. 12.27, AB and CD are two diameters of a circle (with centre O) perpendicular to each other, and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

The radius of larger circle, R = 7 cm

The radius of smaller circle, r = 7/2 cm

Height of ΔBCA = OC = 7 cm

Base of ΔBCA = AB = 14 cm

Area of ΔBCA = 1/2 × AB × OC = (½)×7×14 = 49 cm 2

Area of larger circle = πR 2 = (22/7)×7 2 = 154 cm 2

Area of larger semicircle = 154/2 cm 2 = 77 cm 2

Area of smaller circle = πr 2 = (22/7)×(7/2)×(7/2) = 77/2 cm 2

Area of the shaded region = Area of the larger circle – Area of the triangle – Area of the larger semicircle + Area of the smaller circle

Area of the shaded region = (154-49-77+77/2) cm 2

= 133/2 cm 2 = 66.5 cm 2

10. The area of an equilateral triangle ABC is 17320.5 cm 2 . With each vertex of the triangle as the centre, a circle is drawn with a radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region (Use π = 3.14 and √3 = 1.73205).

ABC is an equilateral triangle.

∴ ∠ A = ∠ B = ∠ C = 60°

There are three sectors, each making 60°.

Area of ΔABC = 17320.5 cm 2

⇒ √3/4 ×(side) 2 = 17320.5

⇒ (side) 2 =17320.5×4/1.73205

⇒ (side) 2 = 4×10 4

⇒ side = 200 cm

Radius of the circles = 200/2 cm = 100 cm

Area of the sector = (60°/360°)×π r 2 cm 2

= 1/6×3.14×(100) 2 cm 2

= 15700/3cm 2

Area of 3 sectors = 3×15700/3 = 15700 cm 2

Thus, the area of the shaded region = Area of an equilateral triangle ABC – Area of 3 sectors

= 17320.5-15700 cm 2 = 1620.5 cm 2

11. On a square handkerchief, nine circular designs, each of a radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Number of circular designs = 9

The radius of the circular design = 7 cm

There are three circles on one side of the square handkerchief.

∴ side of the square = 3×diameter of circle = 3×14 = 42 cm

Area of the square = 42×42 cm 2 = 1764 cm 2

Area of the circle = π r 2 = (22/7)×7×7 = 154 cm 2

Total area of the design = 9×154 = 1386 cm 2

Area of the remaining portion of the handkerchief = Area of the square – Total area of the design = 1764 – 1386 = 378 cm 2

12. In Fig. 12.30, OACB is a quadrant of a circle with centre O and a radius 3.5 cm. If OD = 2 cm, find the area of the

(i) quadrant OACB

(ii) shaded region

Radius of the quadrant = 3.5 cm = 7/2 cm

(i) Area of the quadrant OACB = (πR 2 )/4 cm 2

= (22/7)×(7/2)×(7/2)/4 cm 2

= 77/8 cm 2

(ii) Area of the triangle BOD = (½)×(7/2)×2 cm 2

Area of the shaded region = Area of the quadrant – Area of the triangle BOD

= (77/8)-(7/2) cm 2 = 49/8 cm 2

= 6.125 cm 2

13. In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)

Side of square = OA = AB = 20 cm

The radius of the quadrant = OB

OAB is the right-angled triangle

By Pythagoras’ theorem in ΔOAB,

OB 2 = AB 2 +OA 2

⇒ OB 2 = 20 2 +20 2

⇒ OB 2 = 400+400

⇒ OB 2 = 800

⇒ OB= 20√2 cm

Area of the quadrant = (πR 2 )/4 cm 2 = (3.14/4)×(20√2) 2 cm 2 = 628cm 2

Area of the square = 20×20 = 400 cm 2

Area of the shaded region = Area of the quadrant – Area of the square

= 628-400 cm 2 = 228cm 2

14. AB and CD are, respectively, arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region.

The radius of the larger circle, R = 21 cm

The radius of the smaller circle, r = 7 cm

Angle made by sectors of both concentric circles = 30°

Area of the larger sector = (30°/360°)×πR 2 cm 2

= (1/12)×(22/7)×21 2 cm 2

= 231/2cm 2

Area of the smaller circle = (30°/360°)×πr 2 cm 2

= 1/12×22/7×7 2 cm 2

Area of the shaded region = (231/2) – (77/6) cm 2

= 616/6 cm 2 = 308/3cm 2

15. In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm, and a semicircle is drawn with BC as a diameter. Find the area of the shaded region .

The radius of the quadrant ABC of the circle = 14 cm

AB = AC = 14 cm

BC is the diameter of the semicircle.

ABC is the right-angled triangle.

By Pythagoras’ theorem in ΔABC,

BC 2 = AB 2 +AC 2

⇒ BC 2 = 14 2 +14 2

⇒ BC = 14√2 cm

Radius of the semicircle = 14√2/2 cm = 7√2 cm

Area of the ΔABC =( ½)×14×14 = 98 cm 2

Area of the quadrant = (¼)×(22/7)×(14×14) = 154 cm 2

Area of the semicircle = (½)×(22/7)×7√2×7√2 = 154 cm 2

Area of the shaded region =Area of the semicircle + Area of the ΔABC – Area of the quadrant

= 154 +98-154 cm 2 = 98cm 2

16. Calculate the area of the designed region in Fig. 12.34 common between the two quadrants of circles of radius 8 cm each.

AB = BC = CD = AD = 8 cm

Area of ΔABC = Area of ΔADC = (½)×8×8 = 32 cm 2

Area of quadrant AECB = Area of quadrant AFCD = (¼)×22/7×8 2

= 352/7 cm 2

Area of shaded region = (Area of quadrant AECB – Area of ΔABC) = (Area of quadrant AFCD – Area of ΔADC)

= (352/7 -32)+(352/7- 32) cm 2

= 2×(352/7-32) cm 2

= 256/7 cm 2

The 12th Chapter of NCERT Solutions for Class 10 Maths covers the concepts of the perimeter (circumference) and area of a circle and applies this knowledge in finding the areas of two special ‘parts’ of a circular region known as sector and segment.

Areas Related to Circles is a part of Mensuration, and the unit holds a total weightage of 10 marks in the CBSE exams. In the board examination, one question is sometimes asked from this chapter.

List of Exercises in Class 10 Maths Chapter 12

Exercise 12.1 Solutions (5 Solved Questions)

Exercise 12.2 Solutions (14 Solved Questions)

Exercise 12.3 Solutions (16 Solved Questions)

Chapter 12 of Maths NCERT Solutions for Class 10 is about parts of circles, their measurements and areas of plane figures. BYJU’S subject experts have prepared solutions for each question adhering to the CBSE syllabus (2023-24).

Class 10 Maths NCERT Chapter 12 Area related to circles consists of important topics such as

Key features of ncert solutions for class 10 maths chapter 12 areas related to circles.

• NCERT Solutions help students strengthen their concepts in circle-related areas.
• The solutions are explained using diagrams which make learning more interactive and comprehensive.
• The language used in NCERT Solutions is easy and understandable.
• The step-by-step solving approach helps students to clear their basics.
• Help students solve complex problems at their own pace.

Students can also refer to the NCERT Solutions of other classes and subjects. These solutions are prepared by well-experienced teachers at BYJU’S focusing on providing clarity on key concepts and problem-solving skills.

Students can also get a good grip on the important concepts by referring to other study materials which are provided at BYJU’S.

• RD Sharma Solutions for Class 10 Maths Chapter 15 Areas Related to Circles

Disclaimer – 

Dropped Topics – 

12.1 Introduction 12.2 Perimeter and area of a circle — A review 12.4 Areas of combinations of plane figures

Frequently Asked Questions on NCERT Solutions for Class 10 Maths Chapter 12

What is the importance of studying ncert solutions for class 10 maths chapter 12, mention concepts that are important from an exam perspective in ncert solutions for class 10 maths chapter 12, how many exercises are there in ncert solutions for class 10 maths chapter 12, leave a comment cancel reply.

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Best experience

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

Trial Class

Talk to our experts

1800-120-456-456

• Areas Related to Circles Class 10 Notes CBSE Maths Chapter 12 (Free PDF Download)
• Revision Notes

Exam - Focused Revision Notes for CBSE Class 10 Maths Chapter 12 - Areas Related to Circles

We will analyze the Introduction of Area Related to circles in this chapter and also find the equation of any circle whose centre and radius are given. We’ll find the circumference, area of a circle and circular paths. Also, we’ll study derivations and understand the formulae for perimeter and area of a sector of a circle. We’ll use the above formula to find the perimeter and the area of a sector. Little deeper into the chapter, we’ll find the areas of some combined figures involving circles, sectors, triangles, squares, rectangles and also solve daily life problems on the basis of perimeters and areas of different plane figures.

The revision notes for Chapter 12 Areas Related to Circles are developed according to the NCERT curriculum by the experts in Vedantu who have vast knowledge on the subject. The solutions are developed in a step by step manner to highlight the important formulas and shortcuts. These Areas Related to Circles Class 10 Notes are carefully designed to provide the students with a great learning experience and to make them understand the concepts much faster. The solutions to the important questions of CBSE Class 10 Maths Notes Chapter 12 Areas Related to Circles are available in free PDF versions, students can use these PDFs at Vedantu. Every NCERT Solution is provided to make the study simple and interesting on Vedantu. Register Online for Class 10 Science tuition on Vedantu.com to score more marks in CBSE board examination. Vedantu.com is No.1 Online Tutoring Company in India Provides you Free PDF download of NCERT Solutions for Class 10 Maths solved by Expert Teachers as per NCERT (CBSE) Book guidelines.

Download CBSE Class 10 Maths Revision Notes 2023-24 PDF

Also, check CBSE Class 10 Maths revision notes for All chapters:

Related Chapters

Access Class 10 Mathematics Chapter 12 – Areas Related to Circles Notes in 30 Minutes

The path of a point moving in such a way that its distance from a fixed point is always the same is called a circle. That fixed point is called the centre of that circle and that path is called the locus of that point. The fixed distance between the centre and path is called the radius of that circle. We can see many examples of circles around us like bangles, round chapatis, dial watch, sun, etc.

Perimeter of a circle – Perimeter is the circumferential length of a closed shape or a polygon. In case of circle, if we travel once around a circle, then the length covered gives us the perimeter of circumference. Circumference of a circle always bears a constant ratio with its diameter, which is denoted by a Greek letter $\pi $. Mathematically,

$\pi =\frac{Circumference}{Diameter}$

$\Rightarrow Circumference=\pi \times diameter$

$\Rightarrow Circumference=\pi \times d$

$\Rightarrow Circumference=\pi \times 2r$ (Where $r$ is the radius of circle and $d=2r$).

Area of a circle – The space covered or occupied by a polygon in a two-dimensional plane is called the area. In case of a circle, it is the space occupied withing its boundary or the perimeter. If, $r$ is the radius of a given circle, then the formula for finding the area is given as;

$Area=\pi \times {{r}^{2}}$

Pi ($\pi $):

The value of $\pi $ was given by the great Indian mathematician Aryabhatta. He gave an approximate value of $\pi $ as $\pi =\frac{62832}{20000}$ which is almost equal to $3.1416$. It should be noted that $\pi $ is an irrational number as its value is non-terminating and non-recurring. For calculation purposes, we often take the value of $\pi $ as $\frac{22}{7}$ which in turn is a rational number.

Semicircle:

When a circle is cut into half along a diameter, semicircle is formed as shown below. Its perimeter consists of length of half a circle and the length of a diameter. If the semicircle is open, then diameter length is not added. If the length of diameter is given by $d$ and radius is given by $r$ then perimeter is given by,

$Perimeter=\pi r+d$ (For closed semicircle)

$Perimeter=\pi r$ (For open semicircle)

And the area of a semicircle is just half the area of a circle and is mathematically given as $\frac{\pi {{r}^{2}}}{2}$.

Similarly, area of a quadrant of a circle is given by $\frac{\pi {{r}^{2}}}{4}$.

Sector of a Circle:

The portion of a circle enclosed within an arc and two radii of that circle is called as sector.

Let us take the central angle between the radii is $\theta $ which is ${{360}^{\circ }}$ for a complete circle. Now let the length of that arc be $l$. Then the length $l$ can be found out using the following relation,

$l=\tfrac{\theta }{{{360}^{\circ }}}\times 2\pi r$.

Now, perimeter of sector is given as $2r+l$.

Similarly, area of sector is given by $\frac{\theta }{{{360}^{\circ }}}\times \pi {{r}^{2}}$.

Segment of a Circle:

The part of the circular region enclosed between a chord and the corresponding arc of that circle is called the segment of a circle. The chord having centre of the circle as a point on it is the diameter and also the longest chord of the circle and divides the circle into two equal halves. When the chord is not the diameter, then the portion consisting the centre of circle is called the major segment and the other region is called the minor segment.

In the diagram above the chord, $BC$ divides the circle in two segments. Such as;

Area of minor segment$=$Area of sector $ABDC$$-$Area of $\Delta ABC$.

And area of major segment$=$Area of circle$-$Area of minor segment.

Here, area of $\Delta ABC$ can be found out using the formula $\frac{1}{2}{{r}^{2}}\sin \theta $.

And the area od sector $ABDC$ is given by $\frac{\theta }{{{360}^{\circ }}}\times \pi {{r}^{2}}$.

Hence, the area of segment $ACB=\left( \frac{\theta }{{{360}^{\circ }}}\times \pi {{r}^{2}} \right)-\left( \frac{1}{2}{{r}^{2}}\sin \theta  \right)$

$={{r}^{2}}\left[ \frac{\pi \theta }{{{360}^{\circ }}}-\frac{\sin \theta }{2} \right]$.

Area of a Ring:

Ring is the region between two concentric circles having different radii. Let the radius of larger circle be $R$ and radius of smaller circle be $r$.

Hence the area of the ring is given by;

$\pi {{R}^{2}}-\pi {{r}^{2}}$

$=\pi \left( {{R}^{2}}-{{r}^{2}} \right)$.

Comprehensive Revision Notes for CBSE Class 10 Maths Chapter 12: Areas Related to Circles

Areas Related to Circles Class 10 Notes are prepared by Vedantu to help you revise your questions in this chapter. The following chapter presents several new concepts relating to a circle, for example, lines that cross the circle at different points forming components such as tangents, chords and diameters. This chapter helps you create a solid geometry basis for higher education and to achieve good results in the examinations. In real life also circles and their different properties, such as radius, diameter, circumference and area have applications.

So, the Introduction of Area Related to circles chapter is one of the important topics for Class 10 students from in higher studies point of view. Depending upon the properties & applications of the circles, few topics are designed in higher classes. So, let’s look into the important concepts of the circles which are discussed in this chapter:

Introduction

Area of a circle, circumference of a circle.

Segment of a Circle

Minor arc and Major Arc

Sector of a Circle

Angle of a Sector

Length of an arc of a sector

Area of a Sector of a Circle

Area of a Triangle

Area of a Segment of a Circle

Visualizations

Areas of different plane figures

Areas of Combination of Plane figures

A circle is defined as a collection of points separated by a fixed distance, known as the radius, from a fixed point, known as the centre.

When a line and a circle are both in the same plane, the line and circle will not intersect. At a certain point, the line can come close to touching the circle. That kind of line is known as the tangent to the circle. The line is the secant for the circle as it intersects the circle at two points.

Tangent to a Circle

Tangent to a circle is the line that touches the circle at a single point. The point of tangency is the intersection of a tangent and a circle. The tangent is perpendicular to the circle's radius, in which it intersects. Any curved shape can have tangents. Since tangent is a line, it has its own equation.

The tangent will touch the circle only at one point.

We can name the line that contains the radius through a point of contact as ‘normal’ to circle at the point.

Condition of Tangency

The tangent is called only if it touches a curve at a single point. If not it is said to be simply called a line. So depending on the point of tangency, and also where it falls with respect to a circle, we can specify the criteria for tangent as follows:

When the point lies inside of the circle.

When the point lies on the circle.

When the point lies outside of the circle.

The circumference of a circle, also known as its perimeter, is the measurement of the circle's boundary. The area of a circle, on the other hand, determines the region it occupies. The circumference of a circle is its length when we open it and draw a straight line through it. It's normally expressed in units like centimetres or metres.

⇒ Circumference (or) perimeter of a circle = 2πR

Area of a circle is nothing but the region occupied by the circle in a 2D plane. It can be determined by using the formula, A = πr 2 . (Here, r is the radius of a circle) This formula is useful while measuring the area occupied by a circular field or a plot.

Perimeter of Semicircle

The perimeter of a semicircle is nothing but the sum of half of the circumference of a circle and the diameter. We know that the perimeter of a circle is 2πr or πd. So, the perimeter of a semicircle will be ½ (πd) + d or πr + 2r, in which r is the radius.

A sector is a section of a circle between its two radii and the adjacent arc. A semi-circle that represents half a circle is the most common sector of the circle. A circle that has a sector can be further divided into 2 regions called a Major Sector and a Minor Sector. You can find all the important topics explained in CBSE Class 10 Maths Notes Chapter 12 Areas Related to Circles PDF.

Benefits of Studying Vedantu’s Revision Notes:

Mathematics can be a difficult subject for Class 10 students to achieve good grades in, but if they prepare methodically by having revision notes, they can easily achieve more marks in their Maths exam.

Areas Related to Circles Class 10 Notes will assist you in predicting the types of questions that could be asked during the examination.

Solutions are split into various sections of the exam for a better understanding of the subjects.

You can get a better understanding of the topics in simple language with our Revision notes.

Solutions from Vedantu are error-free and well-organized.

The questions are categorised such as short questions, long answer type questions, all the sections of the question paper in your school exams are thoroughly covered. If you solve these exercises extensively using Vedantu platforms as a reference source, you get full conceptual clarity in question and answer format. It is advisable to practise these questions because the activities in this chapter cover the course in-depth and are equally appropriate for quick review right before your exams.

Tips on How to Prepare for Exams Using Chapter 12 Areas Related to Circles

The tips given below will help students to prepare for their exams by using the free PDF of Areas Related to Circles Class 10 Notes available on Vedantu.

Every question should be carefully read before attempting. Since there are some tough questions, there is a risk that we would give the incorrect answer if the questions are not completely understood.

The basic formulas for finding circumference and area should be memorised in the circle chapter since they are fundamental formulas for solving any problems.

Vedantu's Notes PDF includes several exercises and practise problems. To get good grades on your examinations, students can solve and practise these exercises several times.

These solutions and concepts have been developed by Subject Experts to address your questions & doubts at the same time. This strategy will also allow you to increase your studying effectiveness in your self-study hours. For all your queries relating to 'Area Related to Circles,' Vedantu wants to provide you with a one-stop solution. These solutions are truly informative and provide you with realistic tips and tricks for correctly solving problems.

Vedantu's Areas Related to Circles Class 10 Notes for CBSE Maths Chapter 12 offer a comprehensive and valuable resource for students studying this topic. The free PDF download provided by Vedantu is a fantastic opportunity for learners to access high-quality study material without any financial burden. The notes cover essential concepts, formulas, and solved examples, enhancing students' understanding and problem-solving skills. With Vedantu's user-friendly approach, learners can grasp intricate concepts easily, fostering a deeper appreciation for the subject. Whether preparing for exams or seeking clarity on challenging topics, these notes serve as a reliable and effective aid, empowering students to excel in their academic journey.

FAQs on Areas Related to Circles Class 10 Notes CBSE Maths Chapter 12 (Free PDF Download)

1. Why Should I Refer to Vedantu for CBSE Class 10 Maths Notes Chapter 12 Areas Related to Circles?

Ans: Vedantu has a strong faculty with vast experience in teaching Math subjects. Until offering solutions to major issues, these experts conduct extensive research. Subject matter experts developed these solutions and principles to simultaneously answer your concerns and doubts. This technique would also help you research more efficiently during your self-study hours. As a result, when students use the free PDF, they can learn and enjoy the subject.

2. What are the Topics that are Covered in the Introduction of the Area Related to Circles?

Ans: Circles chapter is one of the important chapters which has more weightage in CBSE exams. Around 5% of weightage is given to this chapter in the board exam and also 2-3% weightage is given JEE exams. The chapter covers Introduction, Area of a Circle, Circumference of a Circle, Segment of a Circle, Minor arc and Major Arc, Sector of a Circle, Angle of a Sector, Length of an arc of a sector, Area of a Sector of a Circle, Area of a Triangle, Area of a Segment of a Circle, Visualizations, Areas of different plane figures, Areas of Combination of Plane figures.

3. How can I Access a Free PDF of Areas Related to Circles Class 10 Notes?

Ans: Vedantu provides free PDF solutions to Chapter 12 Areas Related to Circles. If you solve these exercises extensively using Vedantu platforms as a reference source, you get full conceptual clarity in question and answer format. This free PDF also includes additional problems for students to practise alongside the exercise problems.

4. What are some of the important points to remember for Areas Related to Circles Class 10 Notes CBSE Maths Chapter 12?

Here are some of the important points to remember for Areas Related to Circles Class 10 Notes CBSE Maths Chapter 12:

The radius of a circle is the distance from the center of the circle to any point on its circumference.

The diameter of a circle is twice the radius.

The circumference of a circle is the distance around the circle.

The area of a circle is the amount of space enclosed by the circle.

The formula for the circumference of a circle is 2πr.

The formula for the area of a circle is πr².

5. What are some of the properties and applications of circles?

Properties: 

All radii of a circle are equal in length.

All chords of a circle that pass through its center are equal in length.

The angle in a semicircle is a right angle.

The sum of the angles in a triangle inscribed in a circle is 180°.

Applications:

Circles have many applications in the real world, such as:

Sports equipment

Architecture

Engineering

• Andhra Pradesh
• Chhattisgarh
• West Bengal
• Madhya Pradesh
• Maharashtra
• Jammu & Kashmir
• NCERT Books 2022-23
• NCERT Solutions
• NCERT Notes
• NCERT Exemplar Books
• NCERT Exemplar Solution
• States UT Book
• School Kits & Lab Manual
• NCERT Books 2021-22
• NCERT Books 2020-21
• NCERT Book 2019-2020
• NCERT Book 2015-2016
• RD Sharma Solution
• TS Grewal Solution
• DK Goel Solution
• TR Jain Solution
• Selina Solution
• Frank Solution
• ML Aggarwal Solution
• Lakhmir Singh and Manjit Kaur Solution
• I.E.Irodov solutions
• ICSE - Goyal Brothers Park
• ICSE - Dorothy M. Noronhe
• Sandeep Garg Textbook Solution
• Micheal Vaz Solution
• S.S. Krotov Solution
• Evergreen Science
• KC Sinha Solution
• ICSE - ISC Jayanti Sengupta, Oxford
• ICSE Focus on History
• ICSE GeoGraphy Voyage
• ICSE Hindi Solution
• ICSE Treasure Trove Solution
• Thomas & Finney Solution
• SL Loney Solution
• SB Mathur Solution
• P Bahadur Solution
• Narendra Awasthi Solution
• MS Chauhan Solution
• LA Sena Solution
• Integral Calculus Amit Agarwal Solution
• IA Maron Solution
• Hall & Knight Solution
• Errorless Solution
• Pradeep's KL Gogia Solution
• OP Tandon Solutions
• Sample Papers
• Previous Year Question Paper
• Value Based Questions
• CBSE Syllabus
• CBSE MCQs PDF
• Assertion & Reason
• New Revision Notes
• Revision Notes
• HOTS Question
• Marks Wise Question
• Toppers Answer Sheets
• Exam Paper Aalysis
• Concept Map
• CBSE Text Book
• Additional Practice Questions
• Vocational Book
• CBSE - Concept
• KVS NCERT CBSE Worksheets
• Formula Class Wise
• Formula Chapter Wise
• JEE Crash Course
• JEE Previous Year Paper
• Important Info
• JEE Mock Test
• SRM-JEEE Mock Test
• VITEEE Mock Test
• BITSAT Mock Test
• Manipal Engineering Mock Test
• AP EAMCET Previous Year Paper
• COMEDK Previous Year Paper
• GUJCET Previous Year Paper
• KCET Previous Year Paper
• KEAM Previous Year Paper
• Manipal Previous Year Paper
• MHT CET Previous Year Paper
• WBJEE Previous Year Paper
• AMU Previous Year Paper
• TS EAMCET Previous Year Paper
• SRM-JEEE Previous Year Paper
• VITEEE Previous Year Paper
• BITSAT Previous Year Paper
• Crash Course
• Previous Year Paper
• NCERT Based Short Notes
• NCERT Based Tests
• Previous Year Papers
• Quantitative Aptitude
• Numerical Aptitude Data Interpretation
• General Knowledge
• Mathematics
• Agriculture
• Accountancy
• Business Studies
• Political science
• Enviromental Studies
• Mass Media Communication
• Teaching Aptitude
• NAVODAYA VIDYALAYA
• SAINIK SCHOOL (AISSEE)
• Mechanical Engineering
• Electrical Engineering
• Electronics & Communication Engineering
• Civil Engineering
• Computer Science Engineering
• CBSE Board News
• Scholarship Olympiad
• School Admissions
• Entrance Exams
• All Board Updates
• Miscellaneous
• State Wise Books
• Engineering Exam
• STATE WISE BOOKS
• ENGINEERING EXAM
• SCHOLARSHIP OLYMPIAD
• STATE BOOKS

CBSE Class 10 Maths Case Study

CBSE Board has introduced the case study questions for the ongoing academic session 2021-22. The board will ask the paper on the basis of a different exam pattern which has been introduced this year where 50% syllabus is occupied for MCQ for Term 1 exam. Selfstudys has provided below the chapter-wise questions for CBSE Class 10 Maths. Students must solve these case study based problems as soon as they are done with their syllabus. 

These case studies are in the form of Multiple Choice Questions where students need to answer them as asked in the exam. The MCQs are not that difficult but having a deep and thorough understanding of NCERT Maths textbooks are required to answer these. Furthermore, we have provided the PDF File of CBSE Class 10 maths case study 2021-2022.

Class 10 Maths (Formula, Case Based, MCQ, Assertion Reason Question with Solutions)

In order to score good marks in the term 1 exam students must be aware of the Important formulas, Case Based Questions, MCQ and Assertion Reasons with solutions. Solving these types of questions is important because the board will ask them in the Term 1 exam as per the changed exam pattern of CBSE Class 10th.

Important formulas should be necessarily learned by the students because the case studies are solved with the help of important formulas. Apart from that there are assertion reason based questions that are important too. 

Assertion Reasoning is a kind of question in which one statement (Assertion) is given and its reason is given (Explanation of statement). Students need to decide whether both the statement and reason are correct or not. If both are correct then they have to decide whether the given reason supports the statement or not. In such ways, assertion reasoning questions are being solved. However, for doing so and getting rid of confusions while solving. Students are advised to practice these as much as possible.

For doing so we have given the PDF that has a bunch of MCQs questions based on case based, assertion, important formulas, etc. All the Multiple Choice problems are given with detailed explanations.

CBSE Class 10th Case study Questions

Recently CBSE Board has the exam pattern and included case study questions to make the final paper a little easier. However, Many students are nervous after hearing about the case based questions. They should not be nervous because case study are easy and given in the board papers to ease the Class 10th board exam papers. However to answer them a thorough understanding of the basic concepts are important. For which students can refer to the NCERT textbook.

Basically, case study are the types of questions which are developed from the given data. In these types of problems, a paragraph or passage is given followed by the 5 questions that are given to answer . These types of problems are generally easy to answer because the data are given in the passage and students have to just analyse and find those data to answer the questions.

CBSE Class 10th Assertion Reasoning Questions

These types of questions are solved by reading the statement, and given reason. Sometimes these types of problems can make students confused. To understand the assertion and reason, students need to know that there will be one statement that is known as assertion and another one will be the reason, which is supposed to be the reason for the given statement. However, it is students duty to determine whether the statement and reason are correct or not. If both are correct then it becomes important to check, does reason support the statement? 

Moreover, to solve the problem they need to look at the given options and then answer them.

CBSE Class 10 Maths Case Based MCQ

CBSE Class 10 Maths Case Based MCQ are either Multiple Choice Questions or assertion reasons. To solve such types of problems it is ideal to use elimination methods. Doing so will save time and answering the questions will be much easier. Students preparing for the board exams should definitely solve these types of problems on a daily basis.

Also, the CBSE Class 10 Maths MCQ Based Questions are provided to us to download in PDF file format. All are developed as per the latest syllabus of CBSE Class Xth.

Class 10th Mathematics Multiple Choice Questions

Class 10 Mathematics Multiple Choice Questions for all the chapters helps students to quickly revise their learnings, and complete their syllabus multiple times. MCQs are in the form of objective types of questions whose 4 different options are given and one of them is a true answer to that problem. Such types of problems also aid in self assessment.

Case Study Based Questions of class 10th Maths are in the form of passage. In these types of questions the paragraphs are given and students need to find out the given data from the paragraph to answer the questions. The problems are generally in Multiple Choice Questions.

The Best Class 10 Maths Case Study Questions are available on Selfstudys.com. Click here to download for free.

To solve Class 10 Maths Case Studies Questions you need to read the passage and questions very carefully. Once you are done with reading you can begin to solve the questions one by one. While solving the problems you have to look at the data and clues mentioned in the passage.

In Class 10 Mathematics the assertion and reasoning questions are a kind of Multiple Choice Questions where a statement is given and a reason is given for that individual statement. Now, to answer the questions you need to verify the statement (assertion) and reason too. If both are true then the last step is to see whether the given reason support=rts the statement or not.

CBSE Class 10 Exams Finish, When Can You Expect Results? Details Here

CBSE Board Class 10 Information Technology Answer Key 2024 and Question Papers, Download PDF All SETs

CBSE Board Class 10 Computer Applications Answer Key 2024 and Question Papers, Download PDF All SETs

CBSE Class 10 Information Technology Exam 2024 : Most Important Questions Answers for Last-Minute Revision

CBSE Class 10 Computer Applications Exam 2024 : Most Important Questions Answers for Last-Minute Revision

CBSE Board Class 10 Maths Answer Key 2024 and Question Papers, Download PDF All SETs

• NCERT Solutions for Class 12 Maths
• NCERT Solutions for Class 10 Maths
• CBSE Syllabus 2023-24
• Social Media Channels
• Login Customize Your Notification Preferences

• Second click on the toggle icon

Provide prime members with unlimited access to all study materials in PDF format.

Allow prime members to attempt MCQ tests multiple times to enhance their learning and understanding.

Provide prime users with access to exclusive PDF study materials that are not available to regular users.

CBSE Expert

Class 10 Maths: Case Study Questions of Chapter 10 Circles PDF

Case study Questions on the Class 10 Mathematics Chapter 10  are very important to solve for your exam. Class 10 Maths Chapter 10 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 10 Maths Chapter 10 Circles

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Circles Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 10 Circles

Case Study/Passage Based Questions

Smita always finds it confusing with the concepts of tangent and secant of a circle. But this time she has determined herself to get concepts easier. So, she started listing down the differences between tangent and secant of a circle along with their relation. Here, some points in question form are listed by Smita in her notes.

A line that intersects a circle exactly at two points is called (a) Secant (b) Tangent (c) Chord (d) Both (a) and (b)

Answer: (a) Secant

The number of tangents that can be drawn on a circle is (a) 1 (b) 0 (c) 2 (d) Infinite

Answer: (d) Infinite

The number of tangents that can be drawn to a circle from a point, not on it, is (a) 1 (b) 2 (c) 0 (d) Infinite

Answer: (b) 2

Number of secants that can be drawn to a circle from a point on it is (a) infinite (b) 1 (c) 2 (d) 0

Answer: (a) infinite

A line that touches a circle at only one point is called (a) Secant (b) Chord (c) Tangent (d) Diameter

Answer: (c) Tangent

If a tangent is drawn to a circle from an external point, then the radius at the point of contact is perpendicular to the tangent.

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle. (a) 8 cm (b) 4 cm (c) 10 cm (d) 6 cm

Answer: (a) 8 cm

In the given figure, O is the centre of two concentric circles of radii 5 cm and 3 cm. From an external point P tangent, PA and PB are drawn to these circles. If PA = 12 cm, then PB =

(a) 2√10 cm (b) 2√5 cm (c) 4√10 cm (d) 4√5 cm

Answer: (c) 4√10 cm

The diameter of the two concentric circles is 10 cm and 6 cm. AB is the diameter of the bigger circle and BD is the tangent to the smaller circle touching it at D and intersecting the larger circle at P on producing. Find the length of BP.

Answer: (d) 8 cm

Two concentric circles are such that the difference between their radii is 4 cm and the length of the chord of the larger circle which touches the smaller circle is 24 cm. Then the radius of the smaller circle is (a) 16 cm (b) 20 cm (c) 18 cm (d) None of these

Answer: (a) 16 cm

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 10 Circles with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 10 Maths Circles Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

Leave a Comment Cancel reply

Save my name, email, and website in this browser for the next time I comment.

Download India's best Exam Preparation App Now.

Key Features

• Revision Notes
• Important Questions
• Previous Years Questions
• Case-Based Questions
• Assertion and Reason Questions

No thanks, I’m not interested!

Not Able To Find Desired Paper or Worksheet SEARCH

Find papers & worksheets search, class 10 maths areas related to circles case study based question answers.

• Mathematics

• (0) Comments
• 38 Downloads

Related Papers

Click to view more related papers, display_name = "class 11" && $paper->display_name = "class 12") { // echo $paper->display_name." questions papers and worksheets"; } //else { // echo $paper->display_name." sample papers and previous year papers"; //} //>, cbse class 10 maths extra questions, mcq's and hots chapter wise.

Get here all the Important Extra Questions for CBSE Class 10 Maths as free PDF downloads to increase your exam preparation. Here you may find NCERT Important Questions, MCQ, HOTs and Practice for Class 10 Mathematics chapter wise with solutions also. The Class 10 mathematics extra questions have covered all the significant chapters and related important questions. Daily Maths practice will help you to build strong conceptual knowledge about the subject. These questions will act as chapter wise test papers for Class 10 Mathematics. These Important Questions for Class 10 Mathematics, shared by teachers, parents & students,  are as per latest NCERT and CBSE Pattern syllabus and assure great success in achieving high score in Final Examinations

Latest MCQ, HOTs and Extra Questions for CBSE Class 10

class 10 maths chapter 1 mcq class 10 maths chapter 2 mcq class 10 maths chapter 3 mcq class 10 maths chapter 4 mcq class 10 maths chapter 5 mcq class 10 maths chapter 6 mcq class 10 maths chapter 7 mcq class 10 maths chapter 8 mcq class 10 maths chapter 9 mcq class 10 maths chapter 10 mcq class 10 maths chapter 11 mcq class 10 maths chapter 12 mcq class 10 maths chapter 13 mcq class 10 maths chapter 14 mcq class 10 maths chapter 15 mcq class 10 maths chapter 1 hots questions class 10 maths chapter 2 hots questions class 10 maths chapter 3 hots questions class 10 maths chapter 4 hots questions class 10 maths chapter 5 hots questions class 10 maths chapter 6 hots questions class 10 maths chapter 7 hots questions class 10 maths chapter 8 hots questions class 10 maths chapter 9 hots questions class 10 maths chapter 10 hots questions class 10 maths chapter 12 hots questions class 10 maths chapter 13 hots questions class 10 maths chapter 14 hots questions class 10 maths chapter 15 hots questions Real Numbers Class 10th Extra Questions Polynomials Class 10th Extra Questions Pair of Linear Equations in Two Variables Class 10th Extra Questions Quadratic Equations Class 10th Extra Questions Arithmetic Progressions Class 10th Extra Questions Triangles Class 10th Extra Questions Coordinate Geometry Class 10th Extra Questions Introduction to Trigonometry Class 10th Extra Questions Some Applications of Trigonometry Class 10th Extra Questions Circles Class 10th Extra Questions Constructions Class 10th Extra Questions Areas Related to Circles Class 10th Extra Questions Surface Areas and Volumes Class 10th Extra Questions Statistics Class 10th Extra Questions Probability Class 10th Extra Questions

Total Papers :

CBSE Class 10 Maths Syllabus

• Real Numbers
• Polynomials
• Pair of Linear Equations in Two Variables
• Quadratic Equations
• Arithmetic Progressions
• Coordinate Geometry
• Probability
• Introduction to Trigonometry
• Some Applications of Trigonometry
• Constructions
• Area Related to Circles
• Surface Areas and Volumes

UNIT I: NUMBER SYSTEMS

1. REAL NUMBER

Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality.

UNIT II: ALGEBRA

• POLYNOMIALS Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.
• PAIR OF LINEAR EQUATIONS IN TWO VARIABLES Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination. Simple situational problems.
• QUADRATIC EQUATIONS Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.
• ARITHMETIC PROGRESSIONS Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

UNIT III: COORDINATE GEOMETRY Coordinate Geometry Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

UNIT IV: GEOMETRY

• TRIANGLES Definitions, examples, counter examples of similar triangles. 1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. 2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. 3.(Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar. 4.(Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar. 5.(Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
• CIRCLES Tangent to a circle at, point of contact 1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. 2.(Prove) The lengths of tangents drawn from an external point to a circle are equal.

UNIT V: TRIGONOMETRY

• INTRODUCTION TO TRIGONOMETRY Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0° and 90°. Values of the trigonometric ratios of 30°, 45°, and 60°. Relationships between the ratios.
• TRIGONOMETRIC IDENTITIES Proof and applications of the identity sin2A + cos2A = 1 . Only simple identities to be given.
• HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression. (10)Periods Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°.

UNIT VI: MENSURATION

• AREAS RELATED TO CIRCLES Area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only.
• SURFACE AREAS AND VOLUMES Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

UNIT VII: STATISTICS AND PROBABILITY

• STATISTICS Mean, median and mode of grouped data (bimodal situation to be avoided).
• PROBABILITY (10) Periods Classical definition of probability. Simple problems on finding the probability of an event.

PRESCRIBED BOOKS:

• Mathematics - Textbook for class IX - NCERT Publication
• Mathematics - Textbook for class X - NCERT Publication
• Guidelines for Mathematics Laboratory in Schools, class IX - CBSE Publication
• Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication
• Laboratory Manual - Mathematics, secondary stage - NCERT Publication
• Mathematics exemplar problems for class IX, NCERT publication.
• Mathematics exemplar problems for class X, NCERT publication.

Structure of CBSE Maths Sample Paper for Class 10 is

For Preparation of exams students can also check out other resource material

CBSE Class 10 Maths Sample Papers

CBSE Class 10 Maths Worksheets

CBSE Class 10 Maths Question Papers

CBSE Class 10 Maths Test Papers

CBSE Class 10 Maths Revision Notes

Question Bank of Other Subjects of Class 10

Importance of Question Bank for Exam Preparation?

There are many ways to ascertain whether a student has understood the important points and topics of a particular chapter and is he or she well prepared for exams and tests of that particular chapter. Apart from reference books and notes, Question Banks are very effective study materials for exam preparation. When a student tries to attempt and solve all the important questions of any particular subject , it becomes very easy to gauge how much well the topics have been understood and what kind of questions are asked in exams related to that chapter.. Some of the other advantaging factors of Question Banks are as follows

• Since Important questions included in question bank are collections of questions that were asked in previous exams and tests thus when a student tries to attempt them they get a complete idea about what type of questions are usually asked and whether they have learned the topics well enough. This gives them an edge to prepare well for the exam.Students get the clear idea whether the questions framed from any particular chapter are mostly either short or long answer type questions or multiple choice based and also marks weightage of any particular chapter in final exams.
• CBSE Question Banks are great tools to help in analysis for Exams. As it has a collection of important questions that were asked previously in exams thereby it covers every question from most of the important topics. Thus solving questions from the question bank helps students in analysing their preparation levels for the exam. However the practice should be done in a way that first the set of questions on any particular chapter are solved and then solutions should be consulted to get an analysis of their strong and weak points. This ensures that they are more clear about what to answer and what can be avoided on the day of the exam.
• Solving a lot of different types of important questions gives students a clear idea of what are the main important topics of any particular chapter that needs to focussed on from examination perspective and should be emphasised on for revision before attempting the final paper. So attempting most frequently asked questions and important questions helps students to prepare well for almost everything in that subject.
• Although students cover up all the chapters included in the course syllabus by the end of the session, sometimes revision becomes a time consuming and difficult process. Thus, practicing important questions from Question Bank allows students to check the preparation status of each and every small topic in a chapter. Doing that ensures quick and easy insight into all the important questions and topics in each and every individual. Solving the important questions also acts as the revision process.

Question Bank of Other Classes

To Prepare better for CBSE paperclass; ?> " title="Download Free CBSE Papers">Ribblu.com brings to you all the previous years papers & worksheets of subject; ?//> for CBSE paperclass; ?>. This CBSE paper and worksheet can be instrumental in students achieving maximum marks in their exams. These Papers and worksheets help students gain confidence and make them ready to face their school examinations. These Papers and worksheets school wise, covers important concepts from an examination perspective. Students and parents can download all the available papers & worksheets directly in the form of PDF. One can use these papers and worksheets to get extensive practice and familiarise themselves with the format of the question paper.

You can help other users

Be the first to write comment .

Upload papers and the more your paper get downloaded the more you earn the points

You may send papers on email [email protected] along with userid

• Downloaded by: director academics

Rules and regulations for uploads

Write your comment, report this paper, how to earn points.

Upload Papers / Worksheets and Earn 50 Points.

The uploaded material should be original paper or worksheet of any school. Check out some videos on how to upload papers on ribblu

Rate & Review your school and Earn 25 Points.

Review any school that you may be knowing and once your review is approved, you will be credited with 25 points.

Answer on question posted on JustAsk and earn 15 points.

JustAsk is a platform where you can help others to find answers of any question. Share your Knowledge. Answer questions and once approved you will earn 15 points

Complete your profile and earn upto 25 Points.

Edit and complete your user profile and earn points. The more details you submit, the more points you will earn.

Download Ribblu Mobile App and you will (Earn 20 Points) (one time only)

CBSE Schools

• CBSE Schools In Delhi
• CBSE Schools In Noida
• CBSE Schools In Greater Noida
• CBSE Schools In Faridabad
• CBSE Schools In Ghaziabad
• CBSE Schools In Gurgaon
• CBSE Schools In Mumbai
• CBSE Schools In Pune
• CBSE Schools In Bangalore
• CBSE Schools In Hyderabad
• CBSE Schools In Kolkata
• CBSE Schools In Chennai
• CBSE Schools In Patna
• CBSE Schools In Meerut
• CBSE Schools In Kanpur
• CBSE Schools In Indore
• CBSE Schools In Ludhiana
• CBSE Schools In Dehradun

Top Schools

• Schools In Delhi
• Schools In Noida
• Schools In Greater Noida
• Schools In Faridabad
• Schools In Ghaziabad
• Schools In Gurgaon
• Schools In Mumbai
• Schools In Pune
• Schools In Bangalore
• Schools In Hyderabad
• Schools In Kolkata
• Schools In Chennai
• Schools In Patna
• Schools In Meerut
• Schools In Kanpur
• Schools In Indore
• Schools In Ludhiana
• Schools In Dehradun

Other Schools

• Pre Nursery Schools In Noida
• Day Boarding Schools In Noida
• Pre Nursery Schools In Gurgaon
• Pre Nursery Schools In Delhi
• Play Schools In Delhi
• Day Boarding Schools In Delhi

CBSE Papers

• CBSE Class 1 Sample Papers
• CBSE Class 2 Sample Papers
• CBSE Class 3 Sample Papers
• CBSE Class 4 Sample Papers
• CBSE Class 5 Sample Papers
• CBSE Class 6 Sample Papers
• CBSE Class 7 Sample Papers
• CBSE Class 8 Sample Papers

Paper Categories

• Question Bank
• Question Papers
• Revision Notes
• Sample Papers
• Test Papers
• CBSE Class 9 Sample Papers
• CBSE Class 10 Sample Papers
• CBSE Class 11 Sample Papers
• CBSE Class 12 Sample Papers

• NEET Materials
• JEE Materials
• Banking first yr Materials
• TNPSC Materials
• DIPLOMA COURSE Materials
• 5th Standard Materials
• 12th Standard Materials
• 11th Standard Materials
• 10th Standard Materials
• 9th Standard Materials
• 8th Standard Materials
• 7th Standard Materials
• 6th Standard Materials
• 12th Standard CBSE Materials
• 11th Standard CBSE Materials
• 10th Standard CBSE Materials
• 9th Standard CBSE Materials
• 8th Standard CBSE Materials
• 7th Standard CBSE Materials
• 6th Standard CBSE Materials
• Tamilnadu Stateboard
• Scholarship Exams
• Scholarships

CBSE 10th Standard Maths Subject Circles Case Study Questions 2021

By QB365 on 22 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) Number of tangents that can be drawn on a circle is

(iii) Number of tangents that can be drawn to a circle from a point not on it, is

(iv) Number of secants that can be drawn to a circle from a point on it is

(v) A line that touches a circle at only one point is called

(ii) The value of BQ =

(iii) The value of CQ =

(iv) Which of the following is correct?

(v) Radius of the pit is

(iii) The value of PK =

(iv) The value of QY =

(v) Which of the following is true?

(ii) On the basis of which of the following congruency criterion, \(\Delta \mathrm{OAP} \cong \Delta \mathrm{OBP} ?\)

(iii) If \(\angle\) AOB = 150°, then \(\angle\) APB =

(iv) If \(\angle\) APB = 40°, then \(\angle\) BAO =

(v) If \(\angle\) ABO = 45°, then which of the following is correct option?

(iv) PT is a tangent to a circle with centre 0 and diameter = 40 cm. If PT = 21 cm, then OP =

*****************************************

Cbse 10th standard maths subject circles case study questions 2021 answer keys.

(i) (a) (ii) (d) (iii) (b) (iv) (a) (v) (c)

Here in right angled triangle ABC, AB = 6 m and BC= 8 cm. \(\therefore\) By Pythagoras theorem  \(A C=\sqrt{(A B)^{2}+(B C)^{2}}\) \(=\sqrt{(8)^{2}+(6)^{2}}=\sqrt{100}=10 \mathrm{~m}\) Also, AP = x m. (i) (c): AR=AP = xm      ..(1) [Since, length of tangents drawn from an external point are equal] (ii) (b): BQ = BR = AB - AR = (6 - x) m         (Using (1)) (iii) (d): CQ = CP = AC - AP = (10 - x) m Also, CQ = BC - BQ = BC - BR = 8 - (6 - x) = 2 + x (iv) (b): Since, CQ = 10 - x = 2 + x \(\Rightarrow\) 8 = 2x \(\Rightarrow\) x = 4 \(\therefore\)   AR = AP = 4 m, BR = BQ = 2 m and CP = CQ = 6 m Also, OQ. \(\perp\) BQ and OR.l BR \(\therefore\) BROQ is a square. (v) (a): Radius of the circle, OR = BR = 2 cm

Here, AS = 5 cm, BT = 4 cm  [ \(\therefore\) Radii of circles] (i) (c): Since, radius at point of contact is perpendicular to tangent. \(\therefore\) By Pythagoras theorem, we have \(P A=\sqrt{P S^{2}+A S^{2}}=\sqrt{12^{2}+5^{2}}=\sqrt{169}=13 \mathrm{~cm}\) (ii) (b): Again by Pythagoras theorem, we have \(B Q=\sqrt{T Q^{2}+B T^{2}}=\sqrt{3^{2}+4^{2}}=\sqrt{25}=5 \mathrm{~cm}\) (iii) (d): PK = PA + AK = 13 + 5 = 18 cm (iv) (c): QY = BQ - BY = 5 - 4 = 1 cm (v) (c): PS 2 = PA 2 - AS 2 = PA 2 - AK 2 = (PA + AK)(PA - AK) = PK.PX [ \(\because\) AK = AX]

Related 10th Standard CBSE Maths Materials

10th standard cbse syllabus & materials, cbse 10th social science the making of a global world chapter case study question with answers, cbse 10th social science nationalism in india chapter case study question with answers, cbse 10th social science the rise of nationalism in europe chapter case study question with answers, cbse 10th science metals and non metals chapter case study question with answers, cbse 10th science acids, bases and salts chapter case study question with answers, cbse 10th science chemical reactions and equations chapter case study question with answers, class 10th science - our environment case study questions and answers 2022 - 2023, class 10th science - magnetic effects of electric current case study questions and answers 2022 - 2023, class 10th science - electricity case study questions and answers 2022 - 2023, class 10th science - human eye and the colourful world case study questions and answers 2022 - 2023, class 10th science - light reflection and refraction case study questions and answers 2022 - 2023, class 10th science - heredity and evolution case study questions and answers 2022 - 2023, class 10th science - how do organisms reproduce case study questions and answers 2022 - 2023, class 10th science - life processes case study questions and answers 2022 - 2023, class 10th science - periodic classification of elements case study questions and answers 2022 - 2023.

Class VI to XII

Tn state board / cbse, 3000+ q&a's per subject, score high marks.

10th Standard CBSE Study Materials

10th Standard CBSE Subjects