1. Find Segment Lengths in Circles Lesson 10.6

2. Definition When two chords intersect in the interior of a circle, each chord is divided into two segments that are called segments of the chord.

3. Theorem 10.14 Segments of Chords Theorem If two chords intersect in the interior of a circle, then A D B C E (EA x EB) = (EC x ED)

4. Definitions Secant Segment – A segment that contains a chord of a circle, and has exactly one endpoint outside the circle. External Segment- The part of a secant segment that is outside the circle.

5. Theorem 10.15 Segments of Secants Theorem If two secant segments share the same endpoint outside a circle, then E A C B D (EA X EB) = (EC X ED)

6. Theorem 10.16 Segments of Secants and Tangents Theorem If a secant segment and a tangent segment share an endpoint outside a circle, then E A C D (EA) 2 = (EC x ED)

7. Practice (Find x) 5 6 9 x 4 6 3 x

8. 13 x 10 x 12

9. Homework 2-24even, 29-31