1. Segment Lengths in Circles
Find the lengths of segments of chords
Find the lengths of segments of tangents and secants

2. Two chords intersect
INSIDE the circle
Type 1: a
ab = cd d c b

3. Ex: 1 Solve for x. 9 12 6 3
x = 3 x x 2 2
x = 8 x 3 6 2
x = 1

4. Ex: 2 Solve for x.
2x  3x = 12  8 8 12 2x 3x
6x2 = 96
x2 = 16
x = 4

5. EA • EB = EC • ED Two secants intersect Type 2: OUTSIDE the circle E A

6. Ex: 3 Solve for x. B 13 A 7 E 4 C x D 7
(7 + 13) = 4
(4 + x)
x = 31
140 = x
124 = 4x

7. Ex: 4 Solve for x. B x A 5 D 8 6 C E 6
(6 + 8) = 5
(5 + x)
84 = x
x = 11.8
59 = 5x

8. Type 2 (with a twist):
Secant and Tangent C B E A
EA2 = EB • EC

9. x = 36 242 = 12 (12 + x) 576 = 144 + 12x x 12 24 Ex: 5 Solve for x. CB x 12 E 24 A
242 = 12
(12 + x)
x = 36
576 = x

10. Ex: 6 5 B E 15 C x A x2 = 5
(5 + 15)
x2 = 100
x = 10