MK-MO 1995 Problem 2

Let $a,$ $b$ , and $c$ be sides in a triangle, a $h_a,$ $h_b$ , and $h_c$ are the corresponding altitudes. Prove that $h ^ 2_a + h ^ 2_b + h ^ 2_c \leq \frac{3}{4} (a ^ 2 + b ^ 2 + c ^ 2).$ When is the equation valid?