Problem 437: Tangent Circles, Diameter, Chord, Perpendicular, Congruence

The figure shows the circle 1 with diameter AB and circle 2 with diameter AC tangent at A. Line APD is a chord of circle 1, line DFE is perpendicular to AB, the extension of AF intersects circle 1 at G, line GMH is perpendicular to AB, and AM intersects FE at N. Prove that AN and AP are congruent.