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.