{"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$\\text {(A) } 3 + \\frac {\\sqrt {30}}{2} \\qquad \\text {(B) } 3 + \\frac {\\sqrt {69}}{3} \\qquad \\text {(C) } 3 + \\frac {\\sqrt {123}}{4}\\qquad \\text {(D) } \\frac {52}{9}\\qquad \\text {(E) }3 + 2\\sqrt2$\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>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\">\\text {(A) } 3 + \\frac {\\sqrt {30}}{2} \\qquad \\text {(B) } 3 + \\frac {\\sqrt {69}}{3} \\qquad \\text {(C) } 3 + \\frac {\\sqrt {123}}{4}\\qquad \\text {(D) } \\frac {52}{9}\\qquad \\text {(E) }3 + 2\\sqrt2</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": 5, "problem_name": "2004 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12A_p23", "prev": "/problem/04_amc12A_p21"}}