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Arbitrary point in space - construct triangles

Source: ILL 1979 - Problem 75.

June 5, 2011
geometry unsolvedgeometry

Problem Statement

Given an equilateral triangle ABCABC, let MM be an arbitrary point in space. (a)(\text{a}) Prove that one can construct a triangle from the segments MA,MB,MCMA, MB, MC. (b)(\text{b}) Suppose that PP and QQ are two points symmetric with respect to the center OO of ABCABC. Prove that the two triangles constructed from the segments PA,PB,PCPA,PB,PC and QA,QB,QCQA,QB,QC are of equal area.
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