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Inequality with medians

Source: 2019 Belarus Team Selection Test 1.2

September 2, 2019
inequalitiesgeometry

Problem Statement

Points MM and NN are the midpoints of the sides BCBC and ADAD, respectively, of a convex quadrilateral ABCDABCD. Is it possible that AB+CD>max⁡(AM+DM,BN+CN)? AB+CD>\max(AM+DM,BN+CN)?
(Folklore)
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