KöMaL 2013 C1151

An arbitrary interior point $P$ of a convex quadrilateral ABCD is connected to the midpoints $E$, $F$, $G$, $H$ of the sides $AB$, $BC$, $CD$, $DA$, respectively. Prove that the sum of the areas of the quadrilaterals AEPH and CGPF is equal to the sum of the areas of the quadrilaterals BFPE and DHPG . (Any of them may be a degenerate quadrilateral.)