SHARYGIN 2008 Problem 18

(A.Abdullayev, 9--11) Prove that the triangle having sides $a$ , $b$ , $c$ and area $S$ satisfies the inequality $$a^2+b^2+c^2-\frac12(|a-b|+|b-c|+|c-a|)^2\geq 4\sqrt3 S.$$