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Almost equilateral

Source: 2019 AMC 12A #25

February 8, 2019
AMCAMC 12AMC 12 A2019 AMC2019 AMC 12Ageometry

Problem Statement

Let A0B0C0\triangle A_0B_0C_0 be a triangle whose angle measures are exactly 59.99959.999^\circ, 6060^\circ, and 60.00160.001^\circ. For each positive integer nn define AnA_n to be the foot of the altitude from An1A_{n-1} to line Bn1Cn1B_{n-1}C_{n-1}. Likewise, define BnB_n to be the foot of the altitude from Bn1B_{n-1} to line An1Cn1A_{n-1}C_{n-1}, and CnC_n to be the foot of the altitude from Cn1C_{n-1} to line An1Bn1A_{n-1}B_{n-1}. What is the least positive integer nn for which AnBnCn\triangle A_nB_nC_n is obtuse? \phantom{}
<spanclass=latexbold>(A)</span>10<spanclass=latexbold>(B)</span>11<spanclass=latexbold>(C)</span>13<spanclass=latexbold>(D)</span>14<spanclass=latexbold>(E)</span>15<span class='latex-bold'>(A) </span> 10 \qquad <span class='latex-bold'>(B) </span>11 \qquad <span class='latex-bold'>(C) </span> 13\qquad <span class='latex-bold'>(D) </span> 14 \qquad <span class='latex-bold'>(E) </span> 15