Segment Relationships in Circles 12-6 Segment Relationships in Circles Holt McDougal Geometry Holt Geometry

Learning Targets I will find the lengths of segments formed by lines that intersect circles. I will use the lengths of segments in circles to solve problems.

Vocabulary secant segment external secant segment tangent segment

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: Art Application 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 a chord and its perpendicular bisector. 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

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.

In words: ALL times OUTSIDE equals ALL times OUTSIDE

Example 3: Applying the Secant-Secant Product Theorem Find the value of x and the length of each secant segment. all outside all outside 16(7) = (8 + x)8 112 = 64 + 8x 48 = 8x 6 = x 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.

The words ALL times OUTSIDE equals ALL times OUTSIDE still apply, as the entire tangent segment is outside the circle.

Example 4: Applying the Secant-Tangent Product Theorem 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.

Check It Out! Example 4 Find the value of y. DE  DF = DG2 7(7 + y) = 102 49 + 7y = 100 7y = 51

HOMEWORK: Pages 843 – 844, #6 – 14, 16 - 23