http://www.ck12.org Chapter 9. Circles
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.
2.
3.
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◦