Y by Adventure10, Mango247
Prove: If
are the lengths of the angle bisectors of a triangle with perimeter 6, than we have:
![\[\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} \geq 1.\]](//latex.artofproblemsolving.com/a/3/b/a3b68930020ef875ca878592e52a2f3b5261463d.png)

![\[\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} \geq 1.\]](http://latex.artofproblemsolving.com/a/3/b/a3b68930020ef875ca878592e52a2f3b5261463d.png)
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