IMO 1972 LL USS45

Let ABCD be a convex quadrilateral whose diagonals AC and

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IMO 1972 LL USS45

Origin: USS

Problem

Let ABCD be a convex quadrilateral whose diagonals AC and BD intersect at point O. Let a line through O intersect segment AB at M and segment CD at N. Prove that the segment MN is not longer than at least one of the segments AC and BD.