1. Segment Relationships in Circles
12-6
Segment Relationships in Circles
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry
Holt Geometry

2. Warm Up
Solve for x. 1.
2. 3x = 122
3. BC and DC are tangent
to A. Find BC. 4 48 14

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

5. 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

6. Example 2
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

7. Example 3
What if…? Suppose the length of chord AB that the archeologists drew was 12 in. Find PR
AQ  QB = PQ  QR
6 in.
6(6) = 3(QR)
12 = QR
= 15 = PR

8. A is a segment of a secant with at least one endpoint on the circle.
An is a secant segment that lies in the exterior of the circle with one endpoint on the circle.
secant segment
external secant segment
Secant segments:
External secant segments:

10. Example 4: 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

11. Example 5
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

12. A tangent segment is a segment of a tangent with one endpoint on the circle. AB and AC are tangent segments.

14. ML  JL = KL2 20(5) = x2 100 = x2 ±10 = x Example 6:
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.

15. DE  DF = DG2 7(7 + y) = 102 49 + 7y = 100 7y = 51 Example 7
Find the value of y.
DE  DF = DG2
7(7 + y) = 102
49 + 7y = 100
7y = 51

16. Lesson Quiz
1. Find the value of d and the length of each chord.
d = 9
ZV = 17
WY = 18

17. Lesson Quiz
2. Find the value of x and the length of each secant segment.
x = 10
QP = 8
QR = 12