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Part of 1997 Nordic

Problems(1)

4 equal areas from an interior P of a convex quadrilateral

Source: Nordic Mathematical Contest 1997 #2

10/4/2017
Let ABCDABCD be a convex quadrilateral. We assume that there exists a point PP inside the quadrilateral such that the areas of the triangles ABP,BCP,CDPABP, BCP, CDP, and DAPDAP are equal. Show that at least one of the diagonals of the quadrilateral bisects the other diagonal.
geometryarea of trianglediagonalsareaquadrilateral