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circumcenter of triangle AMN belong to segment AC, DM+BN=MN, AB=AD

Source: Belarus TST 2015 7.2

June 9, 2020
geometryCircumcentercyclic quadrilateralequal segments

Problem Statement

Given a cyclic ABCDABCD with AB=ADAB=AD. Points MM and NN are marked on the sides CDCD and BCBC, respectively, so that DM+BN=MNDM+BN=MN. Prove that the circumcenter of the triangle AMNAMN belongs to the segment ACAC.
N.Sedrakian
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