MathNet 2014 Question 97

In a triangle, let $a, b, c$ be the lengths of sides, and $h_a, h_b, h_c$ be the lengths of corresponding heights. Prove that $(\frac{a}{h_a})^2 + (\frac{b}{h_b})^2 + (\frac{c}{h_c})^2 \ge 4$.