OSN 2011 Problem 3

Given an acute triangle $ABC$ , let $l_a$ be the line passing $A$ and perpendicular to $AB$ , $l_b$ be the line passing $B$ and perpendicular to $BC$ , and $l_c$ be the line passing $C$ and perpendicular to $CA$ . Let $D$ be the intersection of $l_b$ and $l_c$ , $E$ be the intersection of $l_c$ and $l_a$ , and $F$ be the intersection of $l_a$ and $l_b$ . Prove that the area of the triangle $DEF$ is at least three times of the area of $ABC$ .