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. Adiameteris
a chord that passes through the center of the circle. The length of a diameter is two times the length of a radius. A
central angleis the angle formed by two radii and whose its 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. Atangentis a line that intersects a circle in exactly one
point. Thepoint of tangencyis the point where the tangent line touches the circle. Asecantis a line that intersects
a circle in two points.
Guided Practice
Find the measure ofx.
Answers:
For all of the above problems we can use the Outside Angle Theorem.
1.x=^125
◦− 27 ◦
2 =98 ◦
2 =^49
◦- 40◦is not the intercepted arc. Be careful! The intercepted arc is 120◦,( 360 ◦− 200 ◦− 40 ◦). Therefore,x=
200 ◦− 120 ◦
2 =
80 ◦
2 =^40◦.
- First, we need to find the other intercepted arc, 360◦− 265 ◦= 95 ◦.x=^265
◦− 95 ◦
2 =
170 ◦
2 =^85◦Practice
Find the value of the missing variable(s).
1.
2.
3.
4.
5.
6.
7.Solve forx.
8.
9.
10.
11.
12.
13.- Prove the Outside Angle Theorem
Given: Secant rays
−→
ABand