KöMaL 2007 B3978

Prove that the following relationship is true in every triangle: 2$R$($s_a$+$s_b$+$s_c$)$\ge a^2$+$b^2$+$c^2$. (where $a$, $b$, $c$ are the sides, $s_a$, $s_b$, $s_c$ are the lengths of the medians and $R$ is the radius of the circumscribed circle.)