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Unformatted text preview: 147 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 1420 (The TwoTangent 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 1421 (The TwoSecant 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 1422 (The TangentSecant 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 1423 (The TwoChord 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.
 Spring '09
 Johnson
 Algebra

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