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Inequality in convex quadrilateral ABCD

Source: Baltic Way 2001

November 17, 2010
inequalitiesgeometry proposedgeometry

Problem Statement

Let ABCDABCD be a convex quadrilateral, and let NN be the midpoint of BCBC. Suppose further that ∠AND=135∘\angle AND=135^{\circ}. Prove that ∣AB∣+∣CD∣+12⋅∣BC∣≥∣AD∣.|AB|+|CD|+\frac{1}{\sqrt{2}}\cdot |BC|\ge |AD|.
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