{"status": "success", "data": {"description_md": "A square region $ABCD$ is externally tangent to the circle with equation $x^2+y^2=1$ at the point $(0,1)$ on the side $CD$.  Vertices $A$ and $B$ are on the circle with equation $x^2+y^2=4$.  What is the side length of this square?\n\n$\\textbf{(A)}\\ \\frac{\\sqrt{10}+5}{10}\\qquad\\textbf{(B)}\\ \\frac{2\\sqrt{5}}{5}\\qquad\\textbf{(C)}\\ \\frac{2\\sqrt{2}}{3}\\qquad\\textbf{(D)}\\ \\frac{2\\sqrt{19}-4}{5}\\qquad\\textbf{(E)}\\ \\frac{9-\\sqrt{17}}{5}$\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>A square region  <span class=\"katex--inline\">ABCD</span>  is externally tangent to the circle with equation  <span class=\"katex--inline\">x^2+y^2=1</span>  at the point  <span class=\"katex--inline\">(0,1)</span>  on the side  <span class=\"katex--inline\">CD</span> .  Vertices  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  are on the circle with equation  <span class=\"katex--inline\">x^2+y^2=4</span> .  What is the side length of this square?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{\\sqrt{10}+5}{10}\\qquad\\textbf{(B)}\\ \\frac{2\\sqrt{5}}{5}\\qquad\\textbf{(C)}\\ \\frac{2\\sqrt{2}}{3}\\qquad\\textbf{(D)}\\ \\frac{2\\sqrt{19}-4}{5}\\qquad\\textbf{(E)}\\ \\frac{9-\\sqrt{17}}{5}</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": "2012 AMC 12A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc12A_p13", "prev": "/problem/12_amc12A_p11"}}