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

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

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

Vocabulary secant segment external secant segment tangent segment

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 = 10 + 7 = 17 GH = 14 + 5 = 19

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 = 6 + 5 = 11 CD = 3.75 + 8 = 11.75

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 12 + 3 = 15 = PR

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.

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 = 64 + 8x 48 = 8x 6 = x ED = 7 + 9 = 16 EG = 8 + 6 = 14

Check It Out! Example 3 Find the value of z and the length of each secant segment. 39(9) = (13 + z)13 351 = 169 + 13z 182 = 13z 14 = z LG = 30 + 9 = 39 JG = 14 + 13 = 27

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

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.

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

Classwork/Homework 12.6 #’s: 1-4, 5-14, 16-21