FKMO 2009 Problem 1

$a,b,c$ are the length of three sides of a triangle. Let $A= \frac{a^2 +bc}{b+c}+\frac{b^2 +ca}{c+a}+\frac{c^2 +ab}{a+b}$ , $B=\frac{1}{\sqrt{(a+b-c)(b+c-a)}}+\frac{1}{\sqrt{(b+c-a)(c+a-b)}}$ $+\frac{1}{\sqrt{(c+a-b)(a+b-c)}}$ . Prove that $AB \ge 9$ .