11 6 Segment Relationships in Circles Warm UpAdd

11 -6 Segment Relationships in Circles Warm Up(Add to Hw) Solve for x. 1. 4 2. 3 x = 122 48 3. BC and DC are tangent to A. Find BC. 14 Holt Geometry

11 -6 Segment Relationships in Circles 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 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. 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 A tangent segment is a segment of a tangent with one endpoint on the circle. AB and AC are tangent segments. 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 P 795 #2 -8 ev Holt Geometry

11 -6 Segment Relationships in Circles Lesson Quiz: Part I 1. Find the value of d and the length of each chord. d=9 ZV = 17 WY = 18 2. Find the diameter of the plate. Holt Geometry

11 -6 Segment Relationships in Circles Lesson Quiz: Part II 3. Find the value of x and the length of each secant segment. x = 10 QP = 8 QR = 12 4. Find the value of a. 8 Holt Geometry