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angle chasing , danube junior geometry 2014

Source: Danube 2014 Junior P3

September 7, 2018
geometryright angleorthocentermidpoints

Problem Statement

Let ABCABC be a triangle with ∠A<90o,AB≠AC\angle A<90^o, AB \ne AC. Denote HH the orthocenter of triangle ABCABC, NN the midpoint of segment [AH][AH], MM the midpoint of segment [BC][BC] and DD the intersection point of the angle bisector of ∠BAC\angle BAC with the segment [MN][MN]. Prove that <ADH=90o<ADH=90^o
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