{"status": "success", "data": {"description_md": "Trapezoid $ABCD$ has $AD||BC$, $BD = 1$, $\\angle DBA = 23^{\\circ}$, and $\\angle BDC = 46^{\\circ}$.  The ratio $BC: AD$ is $9: 5$.  What is $CD$?\n\n$\\textbf{(A)}\\ \\frac {7}{9}\\qquad \\textbf{(B)}\\ \\frac {4}{5}\\qquad \\textbf{(C)}\\ \\frac {13}{15} \\qquad \\textbf{(D)}\\ \\frac {8}{9}\\qquad \\textbf{(E)}\\ \\frac {14}{15}$\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": "<p>Trapezoid  <span class=\"katex--inline\">ABCD</span>  has  <span class=\"katex--inline\">AD||BC</span> ,  <span class=\"katex--inline\">BD = 1</span> ,  <span class=\"katex--inline\">\\angle DBA = 23^{\\circ}</span> , and  <span class=\"katex--inline\">\\angle BDC = 46^{\\circ}</span> .  The ratio  <span class=\"katex--inline\">BC: AD</span>  is  <span class=\"katex--inline\">9: 5</span> .  What is  <span class=\"katex--inline\">CD</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac {7}{9}\\qquad \\textbf{(B)}\\ \\frac {4}{5}\\qquad \\textbf{(C)}\\ \\frac {13}{15} \\qquad \\textbf{(D)}\\ \\frac {8}{9}\\qquad \\textbf{(E)}\\ \\frac {14}{15}</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": "2009 AMC 12B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12B_p17", "prev": "/problem/09_amc12B_p15"}}