AMC 12 2000 Problem 24

right If circular arcs $AC$ and $BC$ have centers at $B$ and $A$, respectively, then there exists a circle tangent to both $\stackrel{\frown}{AC}$ and $\stackrel{\frown}{BC}$, and to $\overline{AB}$. If the length of $\stackrel{\frown}{BC}$ is $12$, then the circumference of the circle is

$\textbf {(A)}\ 24 \textbf {(B)}\ 25 \textbf {(C)}\ 26 \textbf {(D)}\ 27 \textbf {(E)}\ 28$