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.
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
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 = 6 + 5 = 11 CD = 3.75 + 8 = 11.75
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 12 + 3 = 15 = PR
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:
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 = 64 + 8x 48 = 8x 6 = x ED = 7 + 9 = 16 EG = 8 + 6 = 14
Example 5 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.
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.
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
Lesson Quiz 1. Find the value of d and the length of each chord. d = 9 ZV = 17 WY = 18
Lesson Quiz 2. Find the value of x and the length of each secant segment. x = 10 QP = 8 QR = 12