Question 17
Let $a$, $b$, $c$ be the lengths of the sides of a triangle; $r_a$, $r_b$, $r_c$ be the corresponding exradii, respectively, and $r$ be the inradius. Prove that
$$
\frac{a+b+c}{2\sqrt{a^2+b^2+c^2}} \leq \frac{\sqrt{r_a^2+r_b^2+r_c^2}}{r_a+r_b+r_c-3r}
$$
$$
\frac{a+b+c}{2\sqrt{a^2+b^2+c^2}} \leq \frac{\sqrt{r_a^2+r_b^2+r_c^2}}{r_a+r_b+r_c-3r}
$$