MathDB

1

Part of 1988 Kurschak Competition

Problems(1)

PAB,PBC,PCD,PDA has equal area

Source: Kürschák 1988, problem 1

7/20/2014
Prove that if there exists a point PP inside the convex quadrilateral ABCDABCD such that the triangles PABPAB, PBCPBC, PCDPCD, PDAPDA have the same area, then one of the diagonals of ABCDABCD bisects the area of the quadrilateral.
geometrygeometry unsolved