TH-TMO 2009 Problem 8

Let $a, b, c$ be side lengths of a triangle, and define $s =\frac{a+b+c}{2}$ . Prove that $$\frac{2a(2a-s)}{b + c}+\frac{2b(2b - s)}{c + a}+\frac{2c(2c - s)}{a + b}\ge s.$$