KöMaL 2011 A534

The sides of a triangle are $a$, $b$ and $c$, the lengths of the corresponding medians are $s_a$, $s_b$ and $s_c$, respectively. Prove that $\frac{s_as_b}{a^2+b^2} + \frac{s_bs_c}{b^2+c^2} + \frac{s_cs_a}{c^2+a^2} \ge \frac98$.