{"status": "success", "data": {"description_md": "A circle of radius 1 is randomly placed in a $15\\times36$ rectangle $ABCD$ so that the circle lies completely within the rectangle. Given that the probability that the circle will not touch diagonal $AC$ 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 circle of radius 1 is randomly placed in a <span class=\"katex--inline\">15\\times36</span> rectangle <span class=\"katex--inline\">ABCD</span> so that the circle lies completely within the rectangle. Given that the probability that the circle will not touch diagonal <span class=\"katex--inline\">AC</span> 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/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2004 AIME I Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/04_aime_I_p11", "prev": "/problem/04_aime_I_p09"}}