1. Segment Lengths in Circles

3. Go down the chord and multiply
Two chords intersect
INSIDE the circle
Type 1:
part
part
part
part
Emphasize that the chords are NOT congruent or bisected!
Go down the chord and multiply

4. Solve for x. 9 6 x 2
x = 3

5. Find the length of DB. 8 12 2x 3x A D
x = 4 C
DB = 20 B

6. Find the length of AC and DB.
x – 4 x 5 C 10
x = 8
AC = 13
DB = 14 B

7. Two secants intersect
OUTSIDE the circle
Type 2:

8. 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

9. 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

10. x = 6 10 x 4 8 x (x + 10) = (8 + 4) 8 x2+10x = 96 x2 +10x – 96 = 0
Ex: 5 Solve for x. B 10 A x D 4 8 C E x
(x + 10) =
(8 + 4) 8
x2+10x = 96
x = 6
x2 +10x – 96 = 0

11. Type 2 (with a twist):
Secant and Tangent

12. Ex: 5 Solve for x. x 12 24
242 = 12
(12 + x)
x = 36
576 = x

13. Ex: 6 5 15 x x2 = 5
(5 + 15)
x2 = 100
x = 10