Question 17
Suppose $r$, $R$ are the in-radius and circum-radius of triangle $ABC$. Show that
$$
9r \le a \sin B + b \sin C + c \sin A \le \frac{9R}{2}.
$$
with equality in both inequalities iff $ABC$ is equilateral.
$$
9r \le a \sin B + b \sin C + c \sin A \le \frac{9R}{2}.
$$
with equality in both inequalities iff $ABC$ is equilateral.