Hanoi Open Mathematics Competition 2008 Senior Question 8

Consider a convex quadrilateral \(ABCD\). Let \(O=AC\cap BD\). Let \(M,N\) be the centroids of \(\triangle AOB,\triangle COD\), and \(P,Q\) the orthocenters of \(\triangle BOC,\triangle DOA\), respectively. Prove that \(MN\perp PQ\).