1. Objectives
Find the lengths of segments formed by lines that intersect circles.
Use the lengths of segments in circles to solve problems.

3. Example 1: Applying the Chord-Chord Product Theorem
Find the value of x and the length of each chord.
EJ  JF = GJ  JH J
10(7) = 14(x)
70 = 14x
5 = x
EF = = 17
GH = = 19

4. Check It Out! Example 1
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

6. Example 3: 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. Check It Out! Example 3
Find the value of z and the length of each secant segment.
39(9) = (13 + z)13
351 = z
182 = 13z
14 = z
LG = = 39
JG = = 27

9. Example 4: 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.

10. Check It Out! Example 4
Find the value of y.
DE  DF = DG2
7(7 + y) = 102
49 + 7y = 100
7y = 51