1. 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

2. 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.

3. 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 = = 11
CD = = 11.75

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

7. 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.