1. Secants, Tangents, and Angle Measures
9-6
Secants, Tangents, and Angle Measures
Objectives:
To find the measures of angles formed by intersecting secants and tangents in relation to intercepted arcs..

2. Vocabulary
Secant

3. Secant
A line that intersects a circle in exactly two points is called a secant of the circle.
A secant of circle contains a chord of the circle.

4. Theorem 9-11
If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one-half the measure of its intercepted arc.

5. Theorem 9-12
If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

6. Example 1
Find the value of x.
Find the measure of angle AET.

7. Theorem 9-13 Case 1 – Two Secants
If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

8. Example 2

9. Theorem 9-13 Case 2 – A Secant and a Tangent
If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

10. Example 3

11. Theorem 9-13 Case 3 – Two Tangents
If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

12. Example 4