1. Secants, Tangents and Angle Measures

2. Definition - Secant

3. Theorem – Secant-Secant Angle If 2 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.

4. Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20.

5. Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20. By the previous theorem,

6. Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20. By the previous theorem,

7. Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20. By the previous theorem,

8. Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20. By the previous theorem,

9. Example 1 – Secant-Secant Angle Compute the measure of angle 2 if the measurement of arc BC is 30 and for arc AD is 20. By the previous theorem,

10. Example 2 – Secant-Secant Angle Compute the measurement of angle 4

11. Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

12. Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

13. Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

14. Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

15. Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

16. Example 2 – Secant-Secant Angle Compute the measurement of angle 4 By the previous theorem

17. Theory – Secant-Tangent Angle 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.

18. Example 3 – Secant-Tangent Angle Compute the measurement of angle ABC

19. Example 3 – Secant-Tangent Angle Compute the measurement of angle ABC

20. Example 3 – Secant-Tangent Angle Compute the measurement of angle ABC

21. Example 3 – Secant-Tangent Angle Compute the measurement of angle ABC

22. Example 3 – Secant-Tangent Angle Compute the measurement of angle ABC

23. Theorem For any variation of secants and tangents that intersect outside of the circle, the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

24. Example 4 – Secant-Tangent Angle