{"status": "success", "data": {"description_md": "A circle of radius $2$ is centered at $O$. Square $OABC$ has side length $1$. Sides $AB$ and $CB$ are extended past $B$ to meet the circle at $D$ and $E$, respectively. What is the area of the shaded region in the figure, which is bounded by $BD$, $BE$, and the minor arc connecting $D$ and $E$?\n\n<center>\n<img class=\"problem-image\" height=\"248\" src=\"https://latex.artofproblemsolving.com/7/9/c/79c262c3de70ae89ba3efff503f9573d3a8b5f46.png\" width=\"252\"/>\n</center>\n\n$\\mathrm{(A) \\ } \\frac{\\pi}{3}+1-\\sqrt{3}\\qquad \\mathrm{(B) \\ } \\frac{\\pi}{2}(2-\\sqrt{3})\\qquad \\mathrm{(C) \\ } \\pi(2-\\sqrt{3})\\qquad \\mathrm{(D) \\ } \\frac{\\pi}{6}+\\frac{\\sqrt{3}+1}{2}\\qquad \\mathrm{(E) \\ } \\frac{\\pi}{3}-1+\\sqrt{3}$", "description_html": "<p>A circle of radius  <span class=\"katex--inline\">2</span>  is centered at  <span class=\"katex--inline\">O</span> . Square  <span class=\"katex--inline\">OABC</span>  has side length  <span class=\"katex--inline\">1</span> . Sides  <span class=\"katex--inline\">AB</span>  and  <span class=\"katex--inline\">CB</span>  are extended past  <span class=\"katex--inline\">B</span>  to meet the circle at  <span class=\"katex--inline\">D</span>  and  <span class=\"katex--inline\">E</span> , respectively. What is the area of the shaded region in the figure, which is bounded by  <span class=\"katex--inline\">BD</span> ,  <span class=\"katex--inline\">BE</span> , and the minor arc connecting  <span class=\"katex--inline\">D</span>  and  <span class=\"katex--inline\">E</span> ?</p>\n<center>\n<img class=\"problem-image\" height=\"248\" src=\"https://latex.artofproblemsolving.com/7/9/c/79c262c3de70ae89ba3efff503f9573d3a8b5f46.png\" width=\"252\"/>\n</center>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{\\pi}{3}+1-\\sqrt{3}\\qquad \\mathrm{(B) \\ } \\frac{\\pi}{2}(2-\\sqrt{3})\\qquad \\mathrm{(C) \\ } \\pi(2-\\sqrt{3})\\qquad \\mathrm{(D) \\ } \\frac{\\pi}{6}+\\frac{\\sqrt{3}+1}{2}\\qquad \\mathrm{(E) \\ } \\frac{\\pi}{3}-1+\\sqrt{3}</span> </p>\n<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": "2006 AMC 10B Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc10B_p20", "prev": "/problem/06_amc10B_p18"}}