Triangle Inequality IMO Difficult
1961

Problem - 3027
(Weitzenbock's Inequality) Let $a, b, c$, and $S$ be a triangle's three sides' lengths and its area, respectively. Show that $$a^2 + b^2 + c^2 \ge 4\sqrt{3}\cdot S$$

The solution for this problem is available for $0.99. You can also purchase a pass for all available solutions for$99.