16. In a triangle with sides $a, b, c$, there is a semicircle with its diameter on side $c$ and tangent to sides $a$ and $b$. Find the radius of this semicircle.
And $S_{c O A}=\frac{1}{2} b_{\text {r }}$. Adding these two quantities and expressing the area of $\triangle A B C$ according to Heron's formula, we get:
$$
\begin{array}{l}
r=\frac{2}{a+b} \sqrt{p(p-a)(p-b)(p-c)} \text {. } \\
\text { where } p=\frac{1}{2}(a+b+c) .
\end{array}
$$