{"status": "success", "data": {"description_md": "**POTD December 3, 2023**\n**Author:** munch\n\nThree circles each with radius $1$ have their centers chosen randomly and independently from the points making up a circle of radius $2$. The probability that no two of the circles of radius $1$ intersect can be expressed in the form $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$.", "description_html": "<p><strong>POTD December 3, 2023</strong><br/>&#10;<strong>Author:</strong> munch</p>&#10;<p>Three circles each with radius <span class=\"katex--inline\">1</span> have their centers chosen randomly and independently from the points making up a circle of radius <span class=\"katex--inline\">2</span>. The probability that no two of the circles of radius <span class=\"katex--inline\">1</span> intersect can be expressed in the form <span class=\"katex--inline\">\\frac{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;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #14", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}