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## High school geometry

Unit 8: lesson 7, inscribed angles.

- Challenge problems: Inscribed angles
- Inscribed angle theorem proof
- Your answer should be
- an integer, like 6 6 6 6
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a multiple of pi, like 12 pi 12\ \text{pi} 1 2 pi 12, space, start text, p, i, end text or 2 / 3 pi 2/3\ \text{pi} 2 / 3 pi 2, slash, 3, space, start text, p, i, end text

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## Inscribed Angles

## Inscribed Angle Theorem:

The measure of an inscribed angle is half the measure of the intercepted arc.

That is, m ∠ A B C = 1 2 m ∠ A O C .

Here, ∠ A D C ≅ ∠ A B C ≅ ∠ A F C .

Find the measure of the inscribed angle ∠ P Q R .

The measure of the central angle ∠ P O R of the intercepted arc P R ⌢ is 90 ° .

m ∠ P Q R = 1 2 m ∠ P O R = 1 2 ( 90 ° ) = 45 ° .

In a circle, any two inscribed angles with the same intercepted arcs are congruent.

Here, the inscribed angles ∠ L M N and ∠ L P N have the same intercepted arc L N ⌢ .

Therefore, m ∠ L M N = m ∠ L P N = 55 ° .

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## Inscribed Angles

## Inscribed angle

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## Cite This Source

- The Basics of Circles
- Tangents and Secants
- Circles on the Coordinate Plane
- Math Shack Problems
- Best of the Web
- Table of Contents

## Inscribed Angles Examples

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## IMAGES

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## COMMENTS

Solve two challenging problems that apply the inscribed angle theorem to find an arc measure or an arc length. Problem 1. In the figure below

Problem. A circle is centered on point B B BB. Points A A AA, C C CC and D D DD lie on its circumference. If ∠ A B C \blue{\angle ABC} ... Do 4 problems.

An inscribed angle in a circle is formed by two chords that have a common end point on the circle. This common end point is the vertex of the angle. Here, the

Inscribed Angles (practice problems). 262 views 10 months ago. Mr. Robinson's Virtual Math Classroom. Mr. Robinson's Virtual Math Classroom.

How to Find an Inscribed Angle When Given Its Corresponding Arc Degree, ... Try the free Mathway calculator and problem solver below to practice various

SOLUTION: If two inscribed angles of a circle intercept the same arc or congruent arcs, then the angles are congruent. Since ∠C and ∠D both intercept arc AB

The measure of an inscribed angle is equal to half of the measure of the arc it intercepts or subtends. Thus, in particular it does not depend on the location

Here we have an inscribed angle intercepting an arc, so we can bust out the Inscribed Angle Theorem. We know the measure of arc mAB equals 2 × m∠ACB.

Exercise 40 Page 729 - Practice and Problem Solving - 4. Inscribed Angles - For the first part, let's consider a circle and an inscribed angle ∠ FGH such

All rights reserved. LESSON. Problem Solving. Inscribed Angles. 11-4. 1. Find m AB. z z. A. B. C. D. 160°. 2. Find the angle measures of RSTU. (8y J 4)°.