{"status": "success", "data": {"description_md": "**POTD March 5, 2024**\n\n$3$ points $A,B,C$ are randomly chosen on the circumference of a circle. If $A,B,C$ all lie on a semicircle, then the probability that all of the angles of triangle $ABC$ are less than $120^{\\circ}$ can be written as $\\frac{m}{n}$, where $m,n$ are relatively prime positive integers. Find $m+n$.", "description_html": "<p><strong>POTD March 5, 2024</strong></p>&#10;<p><span class=\"katex--inline\">3</span> points <span class=\"katex--inline\">A,B,C</span> are randomly chosen on the circumference of a circle. If <span class=\"katex--inline\">A,B,C</span> all lie on a semicircle, then the probability that all of the angles of triangle <span class=\"katex--inline\">ABC</span> are less than <span class=\"katex--inline\">120^{\\circ}</span> can be written as <span class=\"katex--inline\">\\frac{m}{n}</span>, where <span class=\"katex--inline\">m,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 #87", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}