Let ABCD be a trapezoid, with AB parallel to CD (the vertices are listed in cyclic order). The
diagonals of this trapezoid are perpendicular to one another and intersect at O. The base
angles DAB and CBA are both acute. A point M on the line segment OA is such
that BMD = 90degrees, and a point N on the line segment OB is such that ANC = 90degrees.
Prove that triangles OMN and OBA are similar.