6

Part of 1991 Austrian-Polish Competition

Problems(1)

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

Source: Austrian-Polish 1991

Suppose that there is a point

P

inside a convex quadrilateral

ABCD

such that the triangles

PAB

PBC

PCD

PDA

have equal areas. Prove that one of the diagonals bisects the area of

ABCD

geometryareasarea of a trianglediagonalbisectconvex