CK-12 Geometry-Concepts

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

Vocabulary

Acircleis the set of all points that are the same distance away from a specific point, called thecenter. Aradiusis
the distance from the center to the circle. Achordis a line segment whose endpoints are on a circle. Adiameter
is a chord that passes through the center of the circle. The length of a diameter is two times the length of a radius.
Acentral angleis an angle formed by two radii and whose vertex is at the center of the circle. Aninscribed angle
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 ◦

Interactive Practice

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/112999