{"status": "success", "data": {"description_md": "Let $\\triangle A_0B_0C_0$ be a triangle whose angle measures are exactly $59.999^\\circ$, $60^\\circ$, and $60.001^\\circ$. For each positive integer $n$, define $A_n$ to be the foot of the altitude from $A_{n-1}$ to line $B_{n-1}C_{n-1}$. Likewise, define $B_n$ to be the foot of the altitude from $B_{n-1}$ to line $A_{n-1}C_{n-1}$, and $C_n$ to be the foot of the altitude from $C_{n-1}$ to line $A_{n-1}B_{n-1}$. What is the least positive integer $n$ for which $\\triangle A_nB_nC_n$ is obtuse?\n\n$\\textbf{(A) } 10 \\qquad \\textbf{(B) }11 \\qquad \\textbf{(C) } 13\\qquad \\textbf{(D) } 14 \\qquad \\textbf{(E) } 15$\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 \\triangle A_0B_0C_0 be a triangle whose angle measures are exactly 59.999^\\circ , 60^\\circ , and 60.001^\\circ . For each positive integer n , define A_n to be the foot of the altitude from A_{n-1} to line B_{n-1}C_{n-1} . Likewise, define B_n to be the foot of the altitude from B_{n-1} to line A_{n-1}C_{n-1} , and C_n to be the foot of the altitude from C_{n-1} to line A_{n-1}B_{n-1} . What is the least positive integer n for which \\triangle A_nB_nC_n is obtuse?

\\textbf{(A) } 10 \\qquad \\textbf{(B) }11 \\qquad \\textbf{(C) } 13\\qquad \\textbf{(D) } 14 \\qquad \\textbf{(E) } 15

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": "2019 AMC 12A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/19_amc12A_p24"}}