{"status": "success", "data": {"description_md": "A sphere is inscribed in the tetrahedron whose vertices are $A=(6,0,0), B=(0,4,0), C=(0,0,2),$ and $D=(0,0,0).$ The radius of the sphere is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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 sphere is inscribed in the tetrahedron whose vertices are <span class=\"katex--inline\">A=(6,0,0), B=(0,4,0), C=(0,0,2),</span> and <span class=\"katex--inline\">D=(0,0,0).</span> The radius of the sphere is <span class=\"katex--inline\">m/n,</span> where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Find <span class=\"katex--inline\">m+n.</span></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": "2001 AIME I Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/01_aime_I_p13", "prev": "/problem/01_aime_I_p11"}}