CK-12 Geometry Concepts

http://www.ck12.org Chapter 9. Circles

is an angle with its vertex on the circle and whose sides are chords. Theintercepted arcis the arc that is inside the
inscribed angle and whose endpoints are on the angle. Aninscribed polygonis a polygon where every vertex is on
the circle.

Guided Practice

QuadrilateralABCDis inscribed in
⊙
E. Find:

1.m^6 A

2.m^6 B

3.m^6 C

4.m^6 D

Answers:

First, note thatmAD̂= 105 ◦because the complete circle must add up to 360◦.

1.m^6 A=^12 mBD̂=^12 ( 115 + 86 ) = 100. 5 ◦

2.m^6 B=^12 mAĈ=^12 ( 86 + 105 ) = 95. 5 ◦

3.m^6 C= 180 ◦−m^6 A= 180 ◦− 100. 5 ◦= 79. 5 ◦

4.m^6 D= 180 ◦−m^6 B= 180 ◦− 95. 5 ◦= 84. 5 ◦

Practice

Fill in the blanks.

1. A(n)___ polygon has all its vertices on a circle.


2. The _____ angles of an inscribed quadrilateral are ____.

QuadrilateralABCDis inscribed in

⊙

E. Find:

3.m^6 DBC

4.mBĈ

5.mAB̂

6.m^6 ACD

7.m^6 ADC

8.m^6 ACB

Find the value ofxand/oryin

⊙

A.

9.

10.

11.

Solve forx.

12.

13.

Use the diagram below to find the measures of the indicated angles and arcs in problems 14-19.