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BM median, prove ME = MF

Source: Sharygin Finals 2023 8.4

August 2, 2023
geometrySharygin Geometry OlympiadSharygin 2023

Problem Statement

Let ABCABC be an acute-angled triangle, OO be its circumcenter, BMBM be a median, and BHBH be an altitude. Circles AOBAOB and BHCBHC meet for the second time at point EE, and circles AHBAHB and BOCBOC meet at point FF. Prove that ME=MFME = MF.
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