KMO 1997 Problem 5

Let $a,b,c$ be the side lengths of any triangle $\triangle ABC$ opposite to $A,B$ and $C,$ respectively. Let $x,y,z$ be the length of medians from $A,B$ and $C,$ respectively. If $T$ is the area of $\triangle ABC$ , prove that $\frac{a^2}{x}+\frac{b^2}{y}+\frac{c^2}{z}\ge\sqrt{\sqrt{3}T}$