Circles Unit 6 Lesson 6 Segment Relationships in

Objectives and Student Expectations � TEKS: G 2 B, G 5 A � The

Example: 1 Find the value of x and the length of each chord. EJ

Example: 2 The art department is contracted to construct a wooden moon for a

Example: 2 continued 8 (d – 8) = 9 9 8 d – 64

A secant segment is a segment of a secant with at least one endpoint

Example: 3 Find the value of x and the length of each secant segment.

A tangent segment is a segment of a tangent with one endpoint on the

Example: 4 Find the value of x. ML JL = KL 2 20(5) =

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Objectives and Student Expectations � TEKS: G 2 B, G 5 A � 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 Find the value of x and the length of each chord. EJ JF = GJ JH 10(7) = 14(x) 70 = 14 x J 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 8 d – 64 = 81 8 d = 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 + 8 x H 48 = 8 x 6=x F ED = 7 + 9 = 16 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 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.