2011 AMC 10B Problem 25

Let T_1 be a triangle with sides 2011, 2012, and 2013. For n \ge 1, if T_n = \triangle ABC and D, E, and F are the points of tangency of the incircle of \triangle ABC to the sides AB, BC and AC, respectively, then T_{n+1} is a triangle with side lengths AD, BE, and CF, if it exists. What is the perimeter of the last triangle in the sequence ( T_n )?

\textbf{(A)}\ \frac{1509}{8} \qquad\textbf{(B)}\ \frac{1509}{32} \qquad\textbf{(C)}\ \frac{1509}{64} \qquad\textbf{(D)}\ \frac{1509}{128} \qquad\textbf{(E)}\ \frac{1509}{256}

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