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Equal to the area of the quadrangle

Source: IMO Longlist 1989, Problem 100

September 18, 2008
geometrygeometry unsolved

Problem Statement

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