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Right angle at the midpoint of EF

Source: Baltic Way 2022/13

November 12, 2022
geometry

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with AB<BCAB < BC and AD<DCAD < DC. Let EE and FF be points on the sides BCBC and CDCD, respectively, such that AB=BEAB = BE and AD=DFAD = DF. Let further M denote the midpoint of the segment EFEF. Prove that ∠BMD=90o\angle BMD = 90^o.
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