{"status": "success", "data": {"description_md": "Three circles of radius $1$ are externally tangent to each other and internally tangent to a larger circle. What is the radius of the large circle?\n\n$\\mathrm{(A) \\ } \\frac{2 + \\sqrt{6}}{3} \\qquad \\mathrm{(B) \\ } 2 \\qquad \\mathrm{(C) \\ } \\frac{2 + 3\\sqrt{2}}{2} \\qquad \\mathrm{(D) \\ } \\frac{3 + 2\\sqrt{3}}{3} \\qquad \\mathrm{(E) \\ } \\frac{3 + \\sqrt{3}}{2}$", "description_html": "<p>Three circles of radius  <span class=\"katex--inline\">1</span>  are externally tangent to each other and internally tangent to a larger circle. What is the radius of the large circle?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{2 + \\sqrt{6}}{3} \\qquad \\mathrm{(B) \\ } 2 \\qquad \\mathrm{(C) \\ } \\frac{2 + 3\\sqrt{2}}{2} \\qquad \\mathrm{(D) \\ } \\frac{3 + 2\\sqrt{3}}{3} \\qquad \\mathrm{(E) \\ } \\frac{3 + \\sqrt{3}}{2}</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": "2004 AMC 10B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10B_p17", "prev": "/problem/04_amc10B_p15"}}