10.6: Secants, Tangents, and Angle Measures

1. 10.6: Secants, Tangents, and Angle Measures

2. Secant: A line that intersects a circle in exactly two points. A D B C

3. A 2 D 1 Theorem 10.12: If 2 secants intersect on the interior of a circle, then the measure of an angle formed is ½ the sum of the measures of the arcs intercepted by the angle and its vertical angle. 3 B C

4. 88 5 4 76

5. D B A Theorem 10.13: If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is ½ the measure of its intercepted arc. C E

6. Theorem 10.14: If 2 secants, a secant and a tangent, or 2 tangents intersect in the exterior of a circle, then the measure of the angle formed is ½ the positive difference of the measures of the intercepted arcs. D A A E A D B B B D C C C

7. Ex. Find x. 55 40 6x

8. 55 40 6x

9. 40 A C B

10. 40 360-X A C B X

11. Angle Measures in Circles *Vertex at the center of the circle: Angle is equal to its intercepted arc. *Vertex on the circle: Angle is equal to ½ the measure of its intercepted arc. *Vertex is on the interior of the circle: Angle is equal to ½ the sum of the 2 intercepted arcs. *Vertex is on the exterior of the circle: Angle is equal to ½ the positive difference of the 2 intercepted arcs.

12. Assignment Section 10.6 Pg. 564 #s 12-32, 34-36