1961 IMO Problems/Problem 6
Consider a plane and three non-collinear points on the same side of ; suppose the plane determined by these three points is not parallel to . In plane take three arbitrary points . Let be the midpoints of segments ; Let be the centroid of the triangle . (We will not consider positions of the points such that the points do not form a triangle.) What is the locus of point as range independently over the plane ?
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