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Locus of points for which products of areas are equal

Source: Czech-Polish-Slovak 2005 Q5

April 27, 2013
geometryconicsanalytic geometrytrigonometrygeometry unsolved

Problem Statement

Given a convex quadrilateral ABCDABCD, find the locus of the points PP inside the quadrilateral such that SPAB⋅SPCD=SPBC⋅SPDAS_{PAB}\cdot S_{PCD} = S_{PBC}\cdot S_{PDA} (where SXS_X denotes the area of triangle XX).
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