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2011 AMC 10B Problem 25

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2011 AMC 10B Problem 25AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 4 of 5 · about 8 min · position P21-25

Let T1T_1 be a triangle with sides 2011,2012,2011, 2012, and 20132013 . For n≥1n \ge 1 , if Tn=△ABCT_n = \triangle ABC and D,E,D, E, and FF are the points of tangency of the incircle of △ABC\triangle ABC to the sides AB,BCAB, BC and AC,AC, respectively, then Tn+1T_{n+1} is a triangle with side lengths AD,BE,AD, BE, and CF,CF, if it exists. What is the perimeter of the last triangle in the sequence (Tn)( T_n ) ?

  1. A)

    15098\frac{1509}{8}

  2. B)

    150932\frac{1509}{32}

  3. C)

    150964\frac{1509}{64}

  4. D)

    1509128\frac{1509}{128}

  5. E)

    1509256\frac{1509}{256}

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