IMO 1979 LL VIE75

Origin: VIE

Problem

Given an equilateral triangle ABC, let M be an arbitrary point in space. (a) Prove that one can construct a triangle from the segments MA, MB, MC. (b) Suppose that P and Q are two points symmetric with respect to the center O of ABC. Prove that the two triangles constructed from the segments PA, PB, PC and QA, QB, QC are of equal area.