Geom4 dec 12 - PEM Level C 12 December 2009 Topics in Geometry The Power Theorems Power of a Point Theorems 1(Power Theorem Let P be a given point

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PEM Level C 12 December 2009 Topics in Geometry - The Power Theorems, Power of a Point Theorems: 1. (Power Theorem) Let P be a given point, and let be a line that passes through P and intersecting a given circle at two (not necessarily distinct) points A and B . Then the product PA · PB is constant for any choice of the line . 2. (Two-Chord Power Theorem) Let P be a point inside a circle. Let 1 and 2 be two chords of the circle that intersect at P . Let A 1 and B 1 be the endpoints of 1 , and let A 2 and B 2 be the endpoints of 2 . Then PA 1 · PB 1 = PA 2 · PB 2 . 3. (Two-Tangent Power Theorem) Let P be a point outside a circle. Let 1 and 2 be the two tangents to the circle through P . Let T 1 and T 2 be the points of tangency of 1 and 2 , respectively, to the circle. Then PT 1 = PT 2 . 4. (Tangent-Secant Power Theorem) Let P be a point outside a circle. Let 1 be a tangent to the circle through P , and 2 a secant to the circle through P
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This note was uploaded on 11/15/2010 for the course MATH 100 taught by Professor B during the Spring '09 term at Ateneo de Manila University.

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