{"status": "success", "data": {"description_md": "Let $A_0 = (0,0)$. Distinct points $A_1,A_2,\\ldots$ lie on the $x$-axis, and distinct points $B_1,B_2,\\ldots$ lie on the graph of $y = \\sqrt {x}$. For every positive integer $n$, $A_{n - 1}B_nA_n$ is an equilateral triangle. What is the least $n$ for which the length $A_0A_n\\ge100$?\n\n$\\textbf{(A)}\\ 13\\qquad \\textbf{(B)}\\ 15\\qquad \\textbf{(C)}\\ 17\\qquad \\textbf{(D)}\\ 19\\qquad \\textbf{(E)}\\ 21$<br>\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": "<p>Let <span class=\"katex--inline\">A_0 = (0,0)</span>. Distinct points <span class=\"katex--inline\">A_1,A_2,\\ldots</span> lie on the <span class=\"katex--inline\">x</span>-axis, and distinct points <span class=\"katex--inline\">B_1,B_2,\\ldots</span> lie on the graph of <span class=\"katex--inline\">y = \\sqrt {x}</span>. For every positive integer <span class=\"katex--inline\">n</span>, <span class=\"katex--inline\">A_{n - 1}B_nA_n</span> is an equilateral triangle. What is the least <span class=\"katex--inline\">n</span> for which the length <span class=\"katex--inline\">A_0A_n\\ge100</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 13\\qquad \\textbf{(B)}\\ 15\\qquad \\textbf{(C)}\\ 17\\qquad \\textbf{(D)}\\ 19\\qquad \\textbf{(E)}\\ 21</span><br/></p>&#10;<hr/>&#10;<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2008 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12B_p25", "prev": "/problem/08_amc12B_p23"}}