Indija mo 2011

Let $ABCDEF$ be a convex hexagon in which the diagonals $AD$, $BE$, $CF$ are concurrent at $O$. Suppose the area of triangle $OAF$ is the geometric mean of those of $OAB$ and $OEF$; and the area of triangle $OBC$ is the geometric mean of those of $OAB$ and $OCD$. Prove that the area of triangle $OED$ is the geometric mean of those of $OCD$ and $OEF$.