IMO 1985 LL SWE77

Two equilateral triangles are inscribed in a circle with radius

IMO 1985 LL SWE77

Origin: SWE

Problem

Two equilateral triangles are inscribed in a circle with radius r. Let A be the area of the set consisting of all points interior to both triangles. Prove that 2A \geqr2\sqrt 3.