Heptagon with extremal area
Source: Austrian Federal Competition 2013, part 2, problem 3
June 18, 2013
geometrygeometry proposed
Problem Statement
A square and an equilateral triangle are inscribed in a same circle. The seven vertices form a convex heptagon inscribed in the circle ( might be a hexagon if two vertices coincide). For which positions of the triangle relative to the square does have the largest and smallest area, respectively?