IMO 1971 LL USS51

Suppose that the sides AB and DC of a convex quadrilateral

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IMO 1971 LL USS51

Origin: USS

Problem

Suppose that the sides AB and DC of a convex quadrilateral ABCD are not parallel. On the sides BC and AD, pairs of points (M, N) and (K, L) are chosen such that BM = MN = NC and AK = KL = LD. Prove that the areas of triangles OKM and OLN are different, where O is the intersection point of AB and CD.