{"status": "success", "data": {"description_md": "Let $ABC$ be a triangle where $M$ is the midpoint of $\\overline{AC}$, and $\\overline{CN}$ is the angle bisector of $\\angle{ACB}$ with $N$ on $\\overline{AB}$. Let $X$ be the intersection of the median $\\overline{BM}$ and the bisector $\\overline{CN}$. In addition $\\triangle BXN$ is equilateral with $AC=2$. What is $BX^2$?\n\n$\\textbf{(A)}\\  \\frac{10-6\\sqrt{2}}{7} \\qquad \\textbf{(B)}\\ \\frac{2}{9} \\qquad \\textbf{(C)}\\ \\frac{5\\sqrt{2}-3\\sqrt{3}}{8} \\qquad \\textbf{(D)}\\ \\frac{\\sqrt{2}}{6} \\qquad \\textbf{(E)}\\ \\frac{3\\sqrt{3}-4}{5}$\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\">ABC</span>  be a triangle where  <span class=\"katex--inline\">M</span>  is the midpoint of  <span class=\"katex--inline\">\\overline{AC}</span> , and  <span class=\"katex--inline\">\\overline{CN}</span>  is the angle bisector of  <span class=\"katex--inline\">\\angle{ACB}</span>  with  <span class=\"katex--inline\">N</span>  on  <span class=\"katex--inline\">\\overline{AB}</span> . Let  <span class=\"katex--inline\">X</span>  be the intersection of the median  <span class=\"katex--inline\">\\overline{BM}</span>  and the bisector  <span class=\"katex--inline\">\\overline{CN}</span> . In addition  <span class=\"katex--inline\">\\triangle BXN</span>  is equilateral with  <span class=\"katex--inline\">AC=2</span> . What is  <span class=\"katex--inline\">BX^2</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\  \\frac{10-6\\sqrt{2}}{7} \\qquad \\textbf{(B)}\\ \\frac{2}{9} \\qquad \\textbf{(C)}\\ \\frac{5\\sqrt{2}-3\\sqrt{3}}{8} \\qquad \\textbf{(D)}\\ \\frac{\\sqrt{2}}{6} \\qquad \\textbf{(E)}\\ \\frac{3\\sqrt{3}-4}{5}</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": 5, "problem_name": "2013 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12B_p25", "prev": "/problem/13_amc12B_p23"}}