Question 12
(POL 5) Given a nonequilateral triangle $ABC$, the vertices listed counterclockwise, find the locus of the centroids of the equilateral triangles $A'B'C'$ (the vertices listed counterclockwise) for which the triples of points $A,B',C'$; $A',B,C'$; and $A',B',C$ are collinear.