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maximum area

Source: Austria 1989

July 10, 2009
geometrytrigonometrygeometry unsolved

Problem Statement

We are given a circle k k and nonparallel tangents t1,t2 t_1,t_2 at points P1,P2 P_1,P_2 on k k, respectively. Lines t1 t_1 and t2 t_2 meet at A0 A_0. For a point A3 A_3 on the smaller arc P1P2, P_1 P_2, the tangent t3 t_3 to k k at P3 P_3 meets t1 t_1 at A1 A_1 and t2 t_2 at A2 A_2. How must P3 P_3 be chosen so that the triangle A0A1A2 A_0 A_1 A_2 has maximum area?
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