FKMO 2010 Problem 1

Given an arbitrary triangle $ABC$ , denote by $P,Q,R$ the intersections of the incircle with sides $BC, CA, AB$ respectively. Let the area of triangle $ABC$ be $T$ , and its perimeter $L$ . Prove that the inequality $$\left(\frac {AB}{PQ}\right)^3 +\left(\frac {BC}{QR}\right)^3 +\left(\frac {CA}{RP}\right)^3 \geq \frac {2}{\sqrt {3}} \cdot \frac {L^2}{T}$$ holds.