JBMO 2002 Problem 4

Prove that for all positive real numbers $a,b,c$ the following inequality takes place $$\frac{1}{b(a+b)}+ \frac{1}{c(b+c)}+ \frac{1}{a(c+a)} \geq \frac{27}{2(a+b+c)^2} .$$ Laurentiu Panaitopol, Romania