Thread: Trapezoid with simialr triangles

Hi need help with thie Trapezoid problem. Feel it may involve Pythagoras or ratio of similar triangler, but am hitting a brick wall.
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 angle DAB and CBA are both acute. A point M on the line segment OA is such that angle BMD equals 90 degrees, and a point N on the line segment OB is such that angle ANC equals 90 degrees.. Prove that triangles OMN and OBA are similar.

Any help would be appreciatted.

Someone else already posted this question: Help with this interesting proof (involving a trapezium)

Basically I proved that if this is true, then MN is parallel to AB and CD. But I don't know if that's provable.