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(PAB)=(PBC)=(PCD)=(PDA), P interior of convex ABCD, diagonal bisects area

Source: Austrian-Polish 1991

May 25, 2019
geometryareasarea of a trianglediagonalbisectconvex

Problem Statement

Suppose that there is a point PP inside a convex quadrilateral ABCDABCD such that the triangles PABPAB, PBCPBC, PCDPCD, PDAPDA have equal areas. Prove that one of the diagonals bisects the area of ABCDABCD.
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