Question 39
Let $a$, $b$ and $c$ be the sides of a triangle and $r$, $R$ and $s$ be the inradius, the circumradius and the semiperimeter of the triangle respectively. Prove that
$$
\frac{1}{a+b} + \frac{1}{a+c} + \frac{1}{b+c} \le \frac{r}{16Rs} + \frac{s}{16Rr} + \frac{11}{8s}
$$
$$
\frac{1}{a+b} + \frac{1}{a+c} + \frac{1}{b+c} \le \frac{r}{16Rs} + \frac{s}{16Rr} + \frac{11}{8s}
$$