IMO 1985 LL MON53

For each P inside the triangle ABC, let A(P), B(P), and

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IMO 1985 LL MON53

Origin: MON

Problem

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