BALKAN 2002 Problem 3

Two circles with different radii intersect in two points $A$ and $B$ . Let the common tangents of the two circles be $MN$ and $ST$ such that $M,S$ lie on the first circle, and $N,T$ on the second. Prove that the orthocenters of the triangles $AMN$ , $AST$ , $BMN$ and $BST$ are the four vertices of a rectangle.