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Find P such that area of triangle is as large as possible

Source:

September 13, 2010
geometryanalytic geometryinequalitiesgeometry proposed

Problem Statement

For each PP inside the triangle ABCABC, let A(P),B(P)A(P), B(P), and C(P)C(P) be the points of intersection of the lines AP,BPAP, BP, and CPCP with the sides opposite to A,BA, B, and CC, respectively. Determine PP in such a way that the area of the triangle A(P)B(P)C(P)A(P)B(P)C(P) is as large as possible.