MathDB

5

Part of 2005 Czech-Polish-Slovak Match

Problems(1)

Locus of points for which products of areas are equal

Source: Czech-Polish-Slovak 2005 Q5

4/27/2013
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).
geometryconicsanalytic geometrytrigonometrygeometry unsolved