ISL 1989 Problem 85
Let a regular gon be inscribed in a circle of radius We consider all the triangles whose vertices are from those of the regular gon.
(a) How many triangles among them contain the center of the circle in their interior?
(b) Find the sum of the areas of all those triangles that contain the center of the circle in their interior.
Dataset text AI-MO AoPS. Quoted with source.
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