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Very simple,however beautiful geometry problem

Source: JBMO Shortlist 2014,G4

November 6, 2016
geometrycircumcircle

Problem Statement

Let ABCABC be an acute triangle such that AB≠AC.AB\not=AC.Let MM be the midpoint BC,HBC,H the orthocenter of △ABC\triangle ABC,O1,O_1 the midpoint of AHAH and O2O_2 the circumcenter of △BCH\triangle BCH.. Prove that O1AMO2O_1AMO_2 is a parallelogram.
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