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APMO 2012 #1

Source: APMO 2012 #1

April 2, 2012
geometryinequalitiesalgebrapolynomialinequalities proposed

Problem Statement

Let P P be a point in the interior of a triangle ABC ABC , and let D,E,F D, E, F be the point of intersection of the line AP AP and the side BC BC of the triangle, of the line BP BP and the side CA CA , and of the line CP CP and the side AB AB , respectively. Prove that the area of the triangle ABC ABC must be 6 6 if the area of each of the triangles PFA,PDB PFA, PDB and PEC PEC is 1 1 .
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