2000 AMC 12 Problem 24

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 \qquad \textbf {(B)}\ 25 \qquad \textbf {(C)}\ 26 \qquad \textbf {(D)}\ 27 \qquad \textbf {(E)}\ 28

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.