1. Segment Relationships in Circles
12-6
Segment Relationships in Circles
Holt McDougal Geometry
Holt Geometry

2. Learning Targets
I will find the lengths of segments formed by lines that intersect circles.
I will use the lengths of segments in circles to solve problems.

3. Vocabulary
secant segment
external secant segment
tangent segment

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: Art Application
The art department is contracted to construct a wooden moon for a play. One of the artists creates a sketch of what it needs to look like by drawing a chord and its perpendicular bisector. Find the diameter of the circle used to draw the outer edge of the moon.

7. Example 2 Continued
8  (d – 8) = 9  9
8d – 64 = 81
8d = 145

8. 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.

9. In words: ALL times OUTSIDE equals ALL times OUTSIDE

10. Example 3: Applying the Secant-Secant Product Theorem
Find the value of x and the length of each secant segment.
all
outside
all
outside
16(7) = (8 + x)8
112 = x
48 = 8x
6 = x
ED = = 16
EG = = 14

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

12. The words ALL times OUTSIDE equals ALL times OUTSIDE still apply, as the entire tangent segment is outside the circle.

13. 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.

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

15. HOMEWORK:
Pages 843 – 844, #6 – 14,