Inequality with S
Source: Sharygin contest 2008. The correspondence round. Problem 18
September 3, 2008
inequalitiesgeometrytrigonometrygeometry proposed
Problem Statement
(A.Abdullayev, 9--11) Prove that the triangle having sides , , and area satisfies the inequality
a^2\plus{}b^2\plus{}c^2\minus{}\frac12(|a\minus{}b|\plus{}|b\minus{}c|\plus{}|c\minus{}a|)^2\geq 4\sqrt3 S.