IMO 1974 LL ROM29

Let A, B, C, D be points in space. If for every point M on the

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IMO 1974 LL ROM29

Origin: ROM

Problem

Let A, B, C, D be points in space. If for every point M on the segment AB the sum area(AMC)+area(CMD)+area(DMB) is constant show that the points A, B, C, D lie in the same plane.