{"status": "success", "data": {"description_md": "A circle of radius $1$ is internally tangent to two circles of radius $2$ at points $A$ and $B$, where $AB$ is a diameter of the smaller circle. What is the area of the region, shaded in the picture, that is outside the smaller circle and inside each of the two larger circles? \n\n$\\mathrm{(A) \\ } \\frac{5}{3} \\pi - 3\\sqrt 2\n\\qquad \n\\mathrm{(B) \\ } \\frac{5}{3} \\pi - 2\\sqrt 3\n\\qquad \n\\mathrm{(C) \\ } \\frac{8}{3} \\pi - 3\\sqrt 3\n\\qquad \n\\mathrm{(D) \\ } \\frac{8}{3} \\pi - 3\\sqrt 2\n\\qquad \n\\mathrm{(E) \\ } \\frac{8}{3} \\pi - 2\\sqrt 3$\n\n<center>\n<img class=\"problem-image\" height=\"285\" src=\"https://latex.artofproblemsolving.com/e/8/e/e8e24df11b3220b60a2c429135703825df20a242.png\" width=\"192\"/>\n</center>", "description_html": "<p>A circle of radius  <span class=\"katex--inline\">1</span>  is internally tangent to two circles of radius  <span class=\"katex--inline\">2</span>  at points  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span> , where  <span class=\"katex--inline\">AB</span>  is a diameter of the smaller circle. What is the area of the region, shaded in the picture, that is outside the smaller circle and inside each of the two larger circles?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{5}{3} \\pi - 3\\sqrt 2\n\\qquad \n\\mathrm{(B) \\ } \\frac{5}{3} \\pi - 2\\sqrt 3\n\\qquad \n\\mathrm{(C) \\ } \\frac{8}{3} \\pi - 3\\sqrt 3\n\\qquad \n\\mathrm{(D) \\ } \\frac{8}{3} \\pi - 3\\sqrt 2\n\\qquad \n\\mathrm{(E) \\ } \\frac{8}{3} \\pi - 2\\sqrt 3</span> </p>\n<center>\n<img class=\"problem-image\" height=\"285\" src=\"https://latex.artofproblemsolving.com/e/8/e/e8e24df11b3220b60a2c429135703825df20a242.png\" width=\"192\"/>\n</center>\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": 4, "problem_name": "2004 AMC 10B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/04_amc10B_p24"}}