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

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.

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

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.

Example: 2 continued 8  (d – 8) = 9  9 8d – 64 = 81 8d = 145 or d = 18.125

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 Find the value of x and the length of each secant segment. 16(7) = (8 + x)8 112 = 64 + 8x H 48 = 8x 6 = x ED = 7 + 9 = 16 F EG = 8 + 6 = 14

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

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.