14.7 - Copy - 14-7 The Power Theorems A Definition a...

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Unformatted text preview: 14-7 The Power Theorems A) Definition a. Tangent segment i. If is tangent to a circle at A, then is called a tangent segment from Q to the circle B) Theorem 14-20 (The Two-Tangent Theorem) a. The two tangent segments to a circle from a point of the exterior are congruent and determine congruent angles with the segment from the exterior point to the center b. If then c. Example) i. A point M is 5 cm from the center of a circle with a 6 cm diameter. How long are the tangent segments from the point M? C) Definition a. Secant segment i. If a segment intersects a circle in two points, and exactly one of these is an endpoint of the segment, then the segment is called a secant segment to the circle D) Theorem 14-21 (The Two-Secant Power Theorem) a. Given a circle C, and a point Q of its exterior. Let be a secant line through Q, intersecting C in points R and S; and let be another secant line through Q, intersecting C in points U and T. Then If Then Example) E) Theorem 14-22 (The Tangent-Secant Power Theorem) a. Given a tangent segment to a circle, and a secant line through Q, intersecting the circle in points R and S. Then If Then Example) In the figure, is a tangent segment. Find the power of Q with respect to C. F) Theorem 14-23 (The Two-Chord Power Theorem) a. Let and be chords of the same circle, intersecting at Q. Then If Then Example) Find the power of Q with respect to C. ...
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This note was uploaded on 05/16/2011 for the course ALGEBRA 098 taught by Professor Johnson during the Spring '09 term at Grand Valley State.

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14.7 - Copy - 14-7 The Power Theorems A Definition a...

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