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

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

3. Vocabulary
secant segment
external secant segment
tangent segment

7. 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

8. 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

9. Check It Out! Example 2
What if…? Suppose the length of chord AB that the archeologists drew was 12 in. In this case how much longer is the disk’s diameter compared to the disk on p. 793?
AQ  QB = PQ  QR
6 in.
6(6) = 3(QR)
12 = QR
= 15 = PR

10. A secant segment is a segment of a secant with at least one endpoint on the circle. An external secant segment is a secant segment that lies in the exterior of the circle with one endpoint on the circle.

11. 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

12. 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

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

14. 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.

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

16. Lesson Quiz: Part I
1. Find the value of d and the length of each chord.
d = 9
ZV = 17
WY = 18
2. Find the diameter of the plate.

17. Lesson Quiz: Part II
3. Find the value of x and the length of each secant segment.
x = 10
QP = 8
QR = 12
4. Find the value of a. 8