1. Other Angle Relationships in Circles Section 10.4
Goal:
- To solve problems using angles formed by tangents, chords and lines that intersect a circle.

2. Theorem 10.12
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. C B A

3. Example C B A D

4. Lines Intersecting On, Inside, or Outside a Circle
On the circle Inside the circle Outside the circle
Case Case Case 3
An inscribed angle

5. Lines, or chords, intersecting inside a circle Theorem 10.13
If two chords intersect in the interior of a circle, then the measures of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle. D A C B

6. Chords, intersecting inside a circle ExampleB

7. Lines Intersecting Outside a Circle Three scenarios!
tangent-secant tangent-tangent secant-secant

8. Tangent - Secant
Tangent-Secant A B C

9. Tangent - Tangent
Tangent-Tangent P Q R

10. Secant - Secant
Secant-Secant A D B C

11. Example
Find x: A B C

12. Example
Find x:

13. Example
Find x:

14. Example
Find x: