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ÖMO 2013 Problem 3

    A square and an equilateral triangle are inscribed in a same circle. The seven vertices form a convex heptagon SS inscribed in the circle ( SS might be a hexagon if two vertices coincide). For which positions of the triangle relative to the square does SS have the largest and smallest area, respectively?

    Dataset text AI-MO AoPS. Quoted with source.

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