IMO 1989 LL TUR102

If in a convex quadrilateral ABCD, E and F are the midpoints

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IMO 1989 LL TUR102

Origin: TUR

Problem

If in a convex quadrilateral ABCD, E and F are the midpoints of the sides BC and DA respectively. Show that the sum of the areas of the triangles EDA and FBC is equal to the area of the quadrangle.