KMO 2010 Problem 2

Let $a, b, c$ be positive real numbers such that $ab+bc+ca=1$ . Prove that $$\sqrt{ a^2 + b^2 + \frac{1}{c^2}} + \sqrt{ b^2 + c^2 + \frac{1}{a^2}} + \sqrt{ c^2 + a^2 + \frac{1}{b^2}} \ge \sqrt{33}$$