Find Segment Lengths in Circles Lesson 10.6

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.

Theorem 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)

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.

Theorem 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)

Theorem 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)

Practice (Find x) x x

13 x 10 x 12

Homework 2-24even, 29-31