{"status": "success", "data": {"description_md": "For $135^\\circ < x < 180^\\circ$, points $P=(\\cos x, \\cos^2 x), Q=(\\cot x, \\cot^2 x), R=(\\sin x, \\sin^2 x)$ and $S =(\\tan x, \\tan^2 x)$ are the vertices of a trapezoid. What is $\\sin(2x)$?\n\n$\\textbf{(A)}\\ 2-2\\sqrt{2}\\qquad\\textbf{(B)} 3\\sqrt{3}-6\\qquad\\textbf{(C)}\\ 3\\sqrt{2}-5\\qquad\\textbf{(D)}\\ -\\frac{3}{4}\\qquad\\textbf{(E)}\\ 1-\\sqrt{3}$\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>For  <span class=\"katex--inline\">135^\\circ &lt; x &lt; 180^\\circ</span> , points  <span class=\"katex--inline\">P=(\\cos x, \\cos^2 x), Q=(\\cot x, \\cot^2 x), R=(\\sin x, \\sin^2 x)</span>  and  <span class=\"katex--inline\">S =(\\tan x, \\tan^2 x)</span>  are the vertices of a trapezoid. What is  <span class=\"katex--inline\">\\sin(2x)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 2-2\\sqrt{2}\\qquad\\textbf{(B)} 3\\sqrt{3}-6\\qquad\\textbf{(C)}\\ 3\\sqrt{2}-5\\qquad\\textbf{(D)}\\ -\\frac{3}{4}\\qquad\\textbf{(E)}\\ 1-\\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": "2013 AMC 12B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12B_p21", "prev": "/problem/13_amc12B_p19"}}