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Show that BM + CM > AY [Macedonia JBMO TST 2017, P4]

Source: Macedonia JBMO TST 2017, Problem 4

June 26, 2018
circumcirclegeometryGeometric Inequalities

Problem Statement

In triangle ABCABC, the points XX and YY are chosen on the arc BCBC of the circumscribed circle of ABCABC that doesn't contain AA so that ∡BAX=∡CAY\measuredangle BAX = \measuredangle CAY. Let MM be the midpoint of the segment AXAX. Show that BM+CM>AY.BM + CM > AY.
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