{"status": "success", "data": {"description_md": "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 $\\left(T_n\\right)$?\n\n$\\textbf{(A)}\\ \\frac{1509}{8} \\qquad \\textbf{(B)}\\ \\frac{1509}{32} \\qquad \\textbf{(C)}\\ \\frac{1509}{64} \\qquad \\textbf{(D)}\\ \\frac{1509}{128} \\qquad \\textbf{(E)}\\ \\frac{1509}{256}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2011 AMC 12B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12B_p23", "prev": "/problem/11_amc12B_p21"}}