1. Unit 9 – Circles Acc. Alg/Geo A
Other Angle Relationships in Circles

2. Unit Goals
Use angles formed by tangents and chords to solve problems.

3. Theorem 10.12
If a tangent and chord intersect at a point on the circle, then the measure of each angle formed is ½ of the measure of its intercepted arc.

4. Example
Find the measure of the indicated arc or angle:
140º

5. Example
Find the value of x:

6. Theorem 10.13
If two chords intersect at a point in a circle, then the measure of each angle formed is ½ the sum of the measures of the intercepted arcs.

7. Example
Find the measure of the indicated angle:
20º
70º

8. Example
Find the measure of the indicated angle:
90º
150º

9. Theorem 10.14
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle is ½ the difference of the intercepted arcs.

10. Example
Find the measure of the indicated angle:
94º
50º

11. Example
Find the measure of the indicated angle:
130º
230º

12. Example
Find the measure of the indicated angle:
190º
110º