Problem 355. Circles, Common external tangent, Concyclic points.
Level: High School, College, SAT Prep.

The figure shows circles 1 and 2 with the common external tangents EH and AD. BF is tangent to circle 1 at M, CG is tangent to circle 2 at N. Lines AM and DN meet at P and lines EM and HN meet at Q. Prove that the points M, P, N, and Q are concyclic (lie on a same circle).