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8

Part of 2001 Baltic Way

Problems(1)

Inequality in convex quadrilateral ABCD

Source: Baltic Way 2001

11/17/2010
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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