RMO 2010 Problem 1

Let $ABCDEF$ be a convex hexagon in which diagonals $AD, BE, CF$ are concurrent at $O$ . Suppose $[OAF]$ is geometric mean of $[OAB]$ and $[OEF]$ and $[OBC]$ is geometric mean of $[OAB]$ and $[OCD]$ . Prove that $[OED]$ is the geometric mean of $[OCD]$ and $[OEF]$ . (Here $[XYZ]$ denotes are of $\triangle XYZ$ )