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Midpoint of internal bisector

Source: Ukrainian National Math Olympiad 4th round

October 20, 2014
geometry unsolvedgeometry

Problem Statement

Let MM be the midpoint of the internal bisector ADAD of △ABC\triangle ABC.Circle ω1\omega_1 with diameter ACAC intersects BMBM at EE and circle ω2\omega_2 with diameter ABAB intersects CMCM at FF.Show that B,E,F,CB,E,F,C are concyclic.
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