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Identity - distance from point on circumcircle to vertices

Source: ILL 1979 - Problem 74.

June 5, 2011
geometrycircumcirclefunctiontrigonometrytrig identitiesLaw of Cosinesgeometry proposed

Problem Statement

Given an equilateral triangle ABCABC of side aa in a plane, let MM be a point on the circumcircle of the triangle. Prove that the sum s=MA4+MB4+MC4s = MA^4 +MB^4 +MC^4 is independent of the position of the point MM on the circle, and determine that constant value as a function of aa.
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