Chapter 8.4, Problem 56AE

Inscribed Circle For Problems 55-58, the lines that bisect each angle of a triangle meet in a single point $O$, and the perpendicular distance $r$ from $O$ to each side of the triangle is the same. The circle with center at $O$ and radius $r$ is called the inscribed circle of the triangle (see the figure).

Use the result of Problem 55 and the results of Problem 60 and 61 in Section $8.3$ to show that

$\cot \frac{C}{2}=\frac{s-c}{r}$

where $s=\frac{1}{2}\left(a+b+c\right)$.