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sum of lengths of sides and diagonals >= 2(2+\sqrt2), when (ABCD)=1

Source: Spanish Mathematical Olympiad 1997 P5

July 31, 2018
geometrygeometric inequalityconvex quadrilateral

Problem Statement

Prove that in every convex quadrilateral of area 11, the sum of the lengths of the sides and diagonals is not smaller than 2(2+2)2(2+\sqrt2).
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