{"status": "success", "data": {"description_md": "A truncated cone has horizontal bases with radii $18$ and $2$. A sphere is tangent to the top, bottom, and lateral surface of the truncated cone. What is the radius of the sphere? \n\n$\\mathrm{(A)}\\ 6\\qquad\\mathrm{(B)}\\ 4\\sqrt{5}\\qquad\\mathrm{(C)}\\ 9\\qquad\\mathrm{(D)}\\ 10\\qquad\\mathrm{(E)}\\ 6\\sqrt{3}$\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>A truncated cone has horizontal bases with radii <span class=\"katex--inline\">18</span> and <span class=\"katex--inline\">2</span>. A sphere is tangent to the top, bottom, and lateral surface of the truncated cone. What is the radius of the sphere?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 6\\qquad\\mathrm{(B)}\\ 4\\sqrt{5}\\qquad\\mathrm{(C)}\\ 9\\qquad\\mathrm{(D)}\\ 10\\qquad\\mathrm{(E)}\\ 6\\sqrt{3}</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2004 AMC 12B Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12B_p20", "prev": "/problem/04_amc12B_p18"}}