11 6 Segment Relationships in Circles Objectives Find

11 -6 Segment Relationships in Circles Objectives Find the lengths of segments formed by lines that intersect circles. Use the lengths of segments in circles to solve problems. Holt Geometry

11 -6 Segment Relationships in Circles Holt Geometry

11 -6 Segment Relationships in Circles Example 1: Applying the Chord-Chord Product Theorem Find the value of x and the length of each chord. EJ JF = GJ JH 10(7) = 14(x) 70 = 14 x 5=x EF = 10 + 7 = 17 GH = 14 + 5 = 19 Holt Geometry J

11 -6 Segment Relationships in Circles Check It Out! Example 1 Find the value of x and the length of each chord. DE EC = AE EB 8(x) = 6(5) 8 x = 30 x = 3. 75 AB = 6 + 5 = 11 CD = 3. 75 + 8 = 11. 75 Holt Geometry

11 -6 Segment Relationships in Circles Holt Geometry

11 -6 Segment Relationships in Circles 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 + 8 x 48 = 8 x 6=x ED = 7 + 9 = 16 EG = 8 + 6 = 14 Holt Geometry

11 -6 Segment Relationships in Circles Check It Out! Example 3 Find the value of z and the length of each secant segment. 39(9) = (13 + z)13 351 = 169 + 13 z 182 = 13 z 14 = z LG = 30 + 9 = 39 JG = 14 + 13 = 27 Holt Geometry

11 -6 Segment Relationships in Circles Holt Geometry

11 -6 Segment Relationships in Circles Example 4: Applying the Secant-Tangent Product Theorem Find the value of x. ML JL = KL 2 20(5) = x 2 100 = x 2 ± 10 = x The value of x must be 10 since it represents a length. Holt Geometry

11 -6 Segment Relationships in Circles Check It Out! Example 4 Find the value of y. DE DF = DG 2 7(7 + y) = 102 49 + 7 y = 100 7 y = 51 Holt Geometry