{"status": "success", "data": {"description_md": "Points $B$ and $C$ lie on $\\overline{AD}$. The length of $\\overline{AB}$ is $4$ times the length of $\\overline{BD}$, and the length of $\\overline{AC}$ is $9$ times the length of $\\overline{CD}$. The length of $\\overline{BC}$ is what fraction of the length of $\\overline{AD}$?\n\n$\\textbf{(A)}\\ \\frac {1}{36} \\qquad \\textbf{(B)}\\ \\frac {1}{13} \\qquad \\textbf{(C)}\\ \\frac {1}{10} \\qquad \\textbf{(D)}\\ \\frac {5}{36} \\qquad \\textbf{(E)}\\ \\frac {1}{5}$<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>Points <span class=\"katex--inline\">B</span> and <span class=\"katex--inline\">C</span> lie on <span class=\"katex--inline\">\\overline{AD}</span>. The length of <span class=\"katex--inline\">\\overline{AB}</span> is <span class=\"katex--inline\">4</span> times the length of <span class=\"katex--inline\">\\overline{BD}</span>, and the length of <span class=\"katex--inline\">\\overline{AC}</span> is <span class=\"katex--inline\">9</span> times the length of <span class=\"katex--inline\">\\overline{CD}</span>. The length of <span class=\"katex--inline\">\\overline{BC}</span> is what fraction of the length of <span class=\"katex--inline\">\\overline{AD}</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ \\frac {1}{36} \\qquad \\textbf{(B)}\\ \\frac {1}{13} \\qquad \\textbf{(C)}\\ \\frac {1}{10} \\qquad \\textbf{(D)}\\ \\frac {5}{36} \\qquad \\textbf{(E)}\\ \\frac {1}{5}</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": 2, "problem_name": "2008 AMC 12B Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12B_p09", "prev": "/problem/08_amc12B_p07"}}