KöMaL 2006 A413

Let $O$ be the point of intersection of the diagonals $AC$, $BD$ of a convex quadrilateral ABCD . Let $G_1$ and $G_2$ be the centroids of triangles OAB and OCD , respectively. Let $H_1$ and $H_2$ be the orthocenters of triangles OBC and ODA , respectively. Prove that $G_1 G_2$ is perpendicular to $H_1 H_2$.