Question 78
If $a$, $b$, $c$ are side lengths and $r$ is the radius of the incircle of a triangle, prove that
$$
\frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2} \le \frac{1}{4r^2}.
$$
$$
\frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2} \le \frac{1}{4r^2}.
$$