{"status": "success", "data": {"description_md": "Three mutually tangent spheres of radius $1$ rest on a horizontal plane. A sphere of radius $2$ rests on them. What is the distance from the plane to the top of the larger sphere?\n\n$\\mathrm{(A) \\ } 3+\\dfrac{\\sqrt{30}}{2} \\qquad \\mathrm{(B) \\ } 3+\\dfrac{\\sqrt{69}}{3} \\qquad \\mathrm{(C) \\ } 3+\\dfrac{\\sqrt{123}}{4} \\qquad \\mathrm{(D) \\ } \\dfrac{52}{9} \\qquad \\mathrm{(E) \\ } 3+2\\sqrt{2}$", "description_html": "<p>Three mutually tangent spheres of radius <span class=\"katex--inline\">1</span> rest on a horizontal plane. A sphere of radius <span class=\"katex--inline\">2</span> rests on them. What is the distance from the plane to the top of the larger sphere?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A) \\ } 3+\\dfrac{\\sqrt{30}}{2} \\qquad \\mathrm{(B) \\ } 3+\\dfrac{\\sqrt{69}}{3} \\qquad \\mathrm{(C) \\ } 3+\\dfrac{\\sqrt{123}}{4} \\qquad \\mathrm{(D) \\ } \\dfrac{52}{9} \\qquad \\mathrm{(E) \\ } 3+2\\sqrt{2}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2004 AMC 10A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/04_amc10A_p24"}}