1. Circles Unit 6: Lesson 6 Segment Relationships in Circles Holt Geometry Texas ©2007

2. Objectives and Student Expectations
TEKS: G2B, G5A
The student will make conjectures about angles, lines, polygons and determine the validity of the conjectures.
The student will use geometric patterns to develop algebraic expressions.

4. Example: 1 J EJ  JF = GJ  JH
Find the value of x and the length of each chord. J
EJ  JF = GJ  JH
10(7) = 14(x)
70 = 14x
5 = x
EF = = 17
GH = = 19

5. Example: 2
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 an 18 inch chord and its perpendicular bisector with length of 8 inches. Find the diameter of the circle used to draw the outer edge of the moon.

6. Example: 2 continued 8  (d – 8) = 9  9 8d – 64 = 81 8d = 145
or d =

7. 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. Example: 3
Find the value of x and the length of each secant segment.
16(7) = (8 + x)8
112 = x H
48 = 8x
6 = x
ED = = 16 F
EG = = 14

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

12. Example: 4 ML  JL = KL2 20(5) = x2 100 = x2 ±10 = x
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.