Problem 438: Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Parallel lines

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 (1) DP and MN are congruent, (2) DM and PN are parallel.