Sec. 12.5 Find Segment Lengths in Circles Review Objectives: 1)Find the lengths of segments formed by lines that intersect circles. 2)Use the lengths of segments in circles to solve problems. Vocabulary: secant segment, external secant segment, tangent segment

Note: This theorem is based on the fact that the two triangles, ∆CED and ∆BED are similar. So, AE relates to DE in the same way that CE relates to BE. That is, AE = CE DE BE then use cross products.

Find the value of x and the length of each chord. DE  EC = AE  EB 8(x) = 6(5) 8x = 30 x = 3.75 AB = 6 + 5 = 11 CD = 3.75 + 8 = 11.75

Applying the Secant-Secant Product Theorem Find the value of x and the length of each secant segment. 16(7) = (8 + x)8 112 = 64 + 8x 48 = 8x 6 = x ED = 7 + 9 = 16 EG = 8 + 6 = 14

Applying the Secant-Tangent Product Theorem Find the value of x. ML  JL = KL2 20(5) = x2 100 = x2 ±10 = x The value of x must be 10 since it represents a length.