IMO 1961 Problem 6

Consider a plane $\epsilon$ and three non-collinear points $A,B,C$ on the same side of $\epsilon$ ; suppose the plane determined by these three points is not parallel to $\epsilon$ . In plane $\epsilon$ take three arbitrary points $A',B',C'$ . Let $L,M,N$ be the midpoints of segments $AA', BB', CC'$ ; Let $G$ be the centroid of the triangle $LMN$ . (We will not consider positions of the points $A', B', C'$ such that the points $L,M,N$ do not form a triangle.) What is the locus of point $G$ as $A', B', C'$ range independently over the plane $\epsilon$ ?