1. 6.6
Finding Segment
Lengths

2. ab = cd Chord-Chord Rule: Two chords intersect INSIDE the circle a d c

3. Example 1: 9 12 6 3 x x 2 2
x = 3
x = 8 x 3 6 2
x = 1

4. Example 2: Find x
2x  3x = 12  8 8 12 2x 3x
6x2 = 96
x2 = 16
x = 4

5. Secant-Secant Rule:
OW-OW

6. EA • EB = EC • ED Two secants intersect Secant-Secant Rule:
OUTSIDE the circle
Secant-Secant Rule: E A B C D
EA • EB = EC • ED

7. x = 31 7 (7 + 13) = 4 (4 + x) 140 = 16 + 4x 124 = 4x Example 3: B 13 AC x D 7
(7 + 13) = 4
(4 + x)
x = 31
140 = x
124 = 4x

8. x = 11.8 x 5 8 6 6 (6 + 8) = 5 (5 + x) 84 = 25 + 5x 59 = 5x Example 4:B x A 5 D 8 6 C E 6
(6 + 8) = 5
(5 + x)
x = 11.8
84 = x
59 = 5x

9. When A secant and tangent originate from the same
Secant-Tangent Rule:
When A secant and tangent originate from the same
point OUTSIDE the circle, use O ●W = O ●W.

10. Notice that on the tangent segment, the outside is the whole!
Secant Segment
External
Segment
Tangent Segment

11. A secant and tangent originate from the same point
Secant-Tangent Rule:
A secant and tangent originate from the same point
OUTSIDE the circle C B E A
EA2 = EB • EC

12. Example 5: C B x 12 E 24 A
242 = 12
(12 + x)
x = 36
576 = x

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

14. Given two chords, USE Given two secants OR a tangent and a secant, USE
What you should know by now…
Given two chords, USE
Given two secants OR a tangent and a secant, USE