Τρίτη, 17 Οκτωβρίου 2017

2001 IMO Shortlist G6

Let $ABC$ be a triangle and $P$ an exterior point in the plane of the triangle. Suppose $AP,BP,CP$ meet the sides $BC,CA,AB$ (or extensions thereof) in $D,E, F$, respectively. Suppose further that the areas of triangles $PBD, PCE, PAF$ are all equal. Prove that each of these areas is equal to the area of triangle $ABC$ itself.

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