ÖMO 2010 Problem 6
A diagonal of a convex hexagon is called long if it decomposes the hexagon into two quadrangles. Each pair of long diagonals decomposes the hexagon into two triangles and two quadrangles. Given is a hexagon with the property, that for each decomposition by two long diagonals the resulting triangles are both isosceles with the side of the hexagon as base. Show that the hexagon has a circumcircle.
Dataset text AI-MO AoPS. Quoted with source.
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