ISL 1979 Problem 75

Given an equilateral triangle $ABC$ , let $M$ be an arbitrary point in space. $(\text{a})$ Prove that one can construct a triangle from the segments $MA, MB, MC$ . $(\text{b})$ 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.