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October 15th, 2010, 06:14 PM   #1
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Area Problem

Angle C is a right angle and P is a point in its interior. Through P we draw a line k intersecting the sides of the angle at A and B. If S1 and S2 are the respective areas of Triangle APC and Triangle BPC, prove that (1/S1) + (1/S2) is the same for all lines k through P.
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October 15th, 2010, 11:16 PM   #2
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Let PM and PN be altitudes of triangles APC and BPC respectively.
1/S1 + 1/S2 = (S2 + S1)/(S1S2) = (ACBC/2)/((ACPM/2)(BCPN/2)) = 2/(PMPN) is independent of k.
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