Inequality in Geometry
Source: TST 2014 of Tajikistan
May 20, 2014
inequalitiesgeometryinequalities proposed
Problem Statement
Let , , be side length of a triangle. Prove the inequality
\begin{align*} \sqrt{a^2 + ab + b^2} + \sqrt{b^2 + bc + c^2} + \sqrt{c^2 + ca + a^2} \leq \sqrt{5a^2 + 5b^2 + 5c^2 + 4ab + 4 bc + 4ca}.\end{align*}