Weitzenböck's Inequality

The applet below illustrates a geometric proof of Weitzenböck's Inequality.

For any triangle ABC with sides $a,$ $b,$ $c,$ and the area $S,$

$a^2 + b^2 + c^2 \ge 4\sqrt{3}S.$

This wonderful geometric proof is due to C. Alsina and R. B. Nelsen.

Explanation