{"status": "success", "data": {"description_md": "Triangle $ABC$ has $AB=27$, $BC=25$, and $CA=26$.  Let $I$ denote the intersection of the internal angle bisectors of $\\triangle ABC$.  What is $BI$?\n\n$\\textbf{(A)}\\ 15\\qquad\\textbf{(B)}\\ 5+\\sqrt{26}+3\\sqrt{3}\\qquad\\textbf{(C)}\\ 3\\sqrt{26}\\qquad\\textbf{(D)}\\ \\frac{2}{3}\\sqrt{546}\\qquad\\textbf{(E)}\\ 9\\sqrt{3}$\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>Triangle  <span class=\"katex--inline\">ABC</span>  has  <span class=\"katex--inline\">AB=27</span> ,  <span class=\"katex--inline\">BC=25</span> , and  <span class=\"katex--inline\">CA=26</span> .  Let  <span class=\"katex--inline\">I</span>  denote the intersection of the internal angle bisectors of  <span class=\"katex--inline\">\\triangle ABC</span> .  What is  <span class=\"katex--inline\">BI</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 15\\qquad\\textbf{(B)}\\ 5+\\sqrt{26}+3\\sqrt{3}\\qquad\\textbf{(C)}\\ 3\\sqrt{26}\\qquad\\textbf{(D)}\\ \\frac{2}{3}\\sqrt{546}\\qquad\\textbf{(E)}\\ 9\\sqrt{3}</span> </p>&#10;<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2012 AMC 12A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc12A_p19", "prev": "/problem/12_amc12A_p17"}}