{"status": "success", "data": {"description_md": "Rectangle $ABCD$ has area $2006$.  An ellipse with area $2006\\pi$ passes through $A$ and $C$ and has foci at $B$ and $D$.  What is the perimeter of the rectangle? (The area of an ellipse is $ab\\pi$ where $2a$ and $2b$ are the lengths of the axes.)\n\n$\\mathrm{(A)}\\ \\frac {16\\sqrt {2006}}{\\pi}<br>\\qquad<br>\\mathrm{(B)}\\ \\frac {1003}4<br>\\qquad<br>\\mathrm{(C)}\\ 8\\sqrt {1003}<br>\\qquad<br>\\mathrm{(D)}\\ 6\\sqrt {2006}<br>\\qquad<br>\\mathrm{(E)}\\ \\frac {32\\sqrt {1003}}\\pi$\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>Rectangle  <span class=\"katex--inline\">ABCD</span>  has area  <span class=\"katex--inline\">2006</span> .  An ellipse with area  <span class=\"katex--inline\">2006\\pi</span>  passes through  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">C</span>  and has foci at  <span class=\"katex--inline\">B</span>  and  <span class=\"katex--inline\">D</span> .  What is the perimeter of the rectangle? (The area of an ellipse is  <span class=\"katex--inline\">ab\\pi</span>  where  <span class=\"katex--inline\">2a</span>  and  <span class=\"katex--inline\">2b</span>  are the lengths of the axes.)</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac {16\\sqrt {2006}}{\\pi}\\qquad\\mathrm{(B)}\\ \\frac {1003}4\\qquad\\mathrm{(C)}\\ 8\\sqrt {1003}\\qquad\\mathrm{(D)}\\ 6\\sqrt {2006}\\qquad\\mathrm{(E)}\\ \\frac {32\\sqrt {1003}}\\pi</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": "2006 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc12B_p22", "prev": "/problem/06_amc12B_p20"}}