2011 AMC 12B Problem 22

Let T_1 be a triangle with side lengths 2011, 2012, and 2013. For n \geq 1, if T_n = \Delta ABC and D, E, and F are the points of tangency of the incircle of \Delta 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 \left(T_n\right)?

\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.