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Geometry Mathley 11.1 hexagon inequality

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June 7, 2020
geometric inequalitygeometryhexagon

Problem Statement

Let ABCDEFABCDEF be a hexagon with sides AB,CD,EFAB,CD,EF being equal to mm units, sides BC,DE,FABC,DE, FA being equal to nn units. The diagonals AD,BE,CFAD,BE,CF have lengths x,yx, y, and zz units. Prove the inequality 1xy+1yz+1zx≥3(m+n)2\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx} \ge \frac{3}{(m+ n)^2}
Nguyễn Văn Quý
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