{"status": "success", "data": {"description_md": "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 $( T_n )$?\n\n$\\textbf{(A)}\\ \\frac{1509}{8} \\qquad\\textbf{(B)}\\ \\frac{1509}{32} \\qquad\\textbf{(C)}\\ \\frac{1509}{64} \\qquad\\textbf{(D)}\\ \\frac{1509}{128} \\qquad\\textbf{(E)}\\ \\frac{1509}{256}$", "description_html": "

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 ) ?

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\\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}

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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": 4, "problem_name": "2011 AMC 10B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/11_amc10B_p24"}}