1. Topic 12-4

2. Interior Intersection Theorem

3. Example 1
Find the value of x.

4. Try This!
Find the value of x.

5. Exterior Intersection Theorem
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

6. Example 2
Find the value of x.

7. Example 3
Find the value of x.

8. Chord Product Theorem
If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

9. Example 4
Find the value of x

10. Example 5
Find the value of x

11. Example 6
Find the value of x

12. Secant-Secant Theorem

13. Example 7
Find the value of x

14. Try This!
Find the value of x

15. Secant Tangent Theorem
If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the length of the secant segment and the length of its external segment equals the square of the length of the tangent segment.

16. Example 8
Find the value of x

17. Try This!
Find the value of x