A. 413. Let O be the point of intersection of the diagonals AC, BD of a convex quadrilateral ABCD. Let G1 and G2 be the centroids of triangles OAB and OCD, respectively. Let H1 and H2 be the orthocenters of triangles OBC and ODA, respectively. Prove that G1G2 is perpendicular to H1H2.
(Vietnamese competitoon problem)
Deadline expired on 15 January 2007.