Home Geometry Problems All Problems Visual Index 431-440 Semicircle Solution / comment        By Antonio Gutierrez
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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.


Tangent Circles, Chords, Perpendicular, Parallel