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PM = DN,MN // BC ,AH_|_BC, right triangle (2003 Romania District VII P2)

Source:

May 24, 2020
geometryequal segmentsparallelperpendicularright triangle

Problem Statement

In the right triangle ABCABC ( ∠A=90o\angle A = 90^o), DD is the intersection of the bisector of the angle AA with the side (BC)(BC), and PP and QQ are the projections of the point DD on the sides (AB),(AC)(AB),(AC) respectively . If BQ∩DP={M}BQ \cap DP=\{M\}, CP∩DQ={N}CP \cap DQ=\{N\}, BQ∩CP={H}BQ\cap CP=\{H\}, show that:
a) PM=DNPM = DN b) MN∥BCMN \parallel BC c) AH⊥BCAH \perp BC.
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