IMO Shortlist 1961 problem 6

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Dodao/la: arhiva
2. travnja 2012.
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?
Izvor: Međunarodna matematička olimpijada, shortlist 1961