IMO 1979 LL VIE74

Given an equilateral triangle ABC of side a in a plane, let

imolonglistmathematicsolympiad

IMO 1979 LL VIE74

Origin: VIE

Problem

Given an equilateral triangle ABC of side a in a plane, let M be a point on the circumcircle of the triangle. Prove that the sum s = MA4 + MB4 + MC4 is independent of the position of the point M on the circle, and determine that constant value as a function of a.