2011 AMC 12A Problem 13

Triangle ABC has side-lengths AB = 12, BC = 24, and AC = 18. The line through the incenter of \triangle ABC parallel to \overline{BC} intersects \overline{AB} at M and \overline{AC} at N. What is the perimeter of \triangle AMN?

\textbf{(A)}\ 27 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 33 \qquad \textbf{(D)}\ 36 \qquad \textbf{(E)}\ 42

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