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inequality with midpoint of arc with equal angles

Source: IGO 2014 Junior 5

July 22, 2018
geometrycircumcirclearc midpointgeometric inequality

Problem Statement

Two points X,YX, Y lie on the arc BCBC of the circumcircle of △ABC\triangle ABC (this arc does not contain AA) such that ∠BAX=∠CAY\angle BAX = \angle CAY . Let MM denotes the midpoint of the chord AXAX . Show that BM+CM>AYBM +CM > AY .
by Mahan Tajrobekar
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