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IMO ShortList 2001, geometry problem 6

Source: IMO ShortList 2001, geometry problem 6

September 30, 2004
geometrylinear algebraareaTriangleIMO Shortlist

Problem Statement

Let ABCABC be a triangle and PP an exterior point in the plane of the triangle. Suppose the lines APAP, BPBP, CPCP meet the sides BCBC, CACA, ABAB (or extensions thereof) in DD, EE, FF, respectively. Suppose further that the areas of triangles PBDPBD, PCEPCE, PAFPAF are all equal. Prove that each of these areas is equal to the area of triangle ABCABC itself.
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