{"status": "success", "data": {"description_md": "Quadrilateral $ABCD$ has right angles at $B$ and $C$, $\\triangle ABC \\sim \\triangle BCD$, and $AB > BC$. There is a point $E$ in the interior of $ABCD$ such that $\\triangle ABC \\sim \\triangle CEB$ and the area of $\\triangle AED$ is $17$ times the area of $\\triangle CEB$. What is $\\frac{AB}{BC}$?\n\n$\\textbf{(A)}\\ 1 + \\sqrt{2} \\qquad \\textbf{(B)}\\ 2 + \\sqrt{2} \\qquad \\textbf{(C)}\\ \\sqrt{17} \\qquad \\textbf{(D)}\\ 2 + \\sqrt{5} \\qquad\\textbf{(E)}\\ 1 + 2\\sqrt{3}$\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>Quadrilateral  <span class=\"katex--inline\">ABCD</span>  has right angles at  <span class=\"katex--inline\">B</span>  and  <span class=\"katex--inline\">C</span> ,  <span class=\"katex--inline\">\\triangle ABC \\sim \\triangle BCD</span> , and  <span class=\"katex--inline\">AB &gt; BC</span> . There is a point  <span class=\"katex--inline\">E</span>  in the interior of  <span class=\"katex--inline\">ABCD</span>  such that  <span class=\"katex--inline\">\\triangle ABC \\sim \\triangle CEB</span>  and the area of  <span class=\"katex--inline\">\\triangle AED</span>  is  <span class=\"katex--inline\">17</span>  times the area of  <span class=\"katex--inline\">\\triangle CEB</span> . What is  <span class=\"katex--inline\">\\frac{AB}{BC}</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 1 + \\sqrt{2} \\qquad \\textbf{(B)}\\ 2 + \\sqrt{2} \\qquad \\textbf{(C)}\\ \\sqrt{17} \\qquad \\textbf{(D)}\\ 2 + \\sqrt{5} \\qquad\\textbf{(E)}\\ 1 + 2\\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": 5, "problem_name": "2017 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12B_p25", "prev": "/problem/17_amc12B_p23"}}