MathDB

74

Part of 1979 IMO Longlists

Problems(1)

Identity - distance from point on circumcircle to vertices

Source: ILL 1979 - Problem 74.

6/5/2011
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.
geometrycircumcirclefunctiontrigonometrytrig identitiesLaw of Cosinesgeometry proposed