IMO 1983 LL VIE73

Let ABC be a nonequilateral triangle. Prove that there exist

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IMO 1983 LL VIE73

Origin: VIE

Problem

Let ABC be a nonequilateral triangle. Prove that there exist two points P and Q in the plane of the triangle, one in the interior and one in the exterior of the circumcircle of ABC, such that the orthogonal projections of any of these two points on the sides of the triangle are vertices of an equilateral triangle.