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Show that angle ADO = angle HAN

Source: JMO 2017 P5

April 20, 2017
USAJMOgeometry

Problem Statement

Let OO and HH be the circumcenter and the orthocenter of an acute triangle ABCABC. Points MM and DD lie on side BCBC such that BM=CMBM=CM and ∠BAD=∠CAD\angle BAD = \angle CAD. Ray MOMO intersects the circumcircle of triangle BHCBHC in point NN. Prove that ∠ADO=∠HAN\angle ADO = \angle HAN.
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