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Lengths of the angle bisectors of a triangle with perimeter

Source: VAIMO 2, German Pre-TST 2002

July 17, 2011
geometryperimetergeometry unsolved

Problem Statement

Prove: If x,y,zx, y, z are the lengths of the angle bisectors of a triangle with perimeter 6, than we have:
1x2+1y2+1z2≥1.\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} \geq 1.
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