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Easy geometric inequality

Source: III Caucasus Mathematical Olympiad

March 17, 2018
geometrygeometric inequalityinequalities

Problem Statement

Given a convex quadrilateral ABCDABCD with ∠BCD=90∘\angle BCD=90^\circ. Let EE be the midpoint of ABAB. Prove that 2EC⩽AD+BD2EC \leqslant AD+BD.
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