Areas of all triangles that contain center of the circle
Source: IMO Longlist 1989, Problem 85
September 18, 2008
geometrygeometry unsolved
Problem Statement
Let a regular (2n \plus{}1)\minus{}gon be inscribed in a circle of radius We consider all the triangles whose vertices are from those of the regular (2n \plus{} 1)\minus{}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.