{"status": "success", "data": {"description_md": "**POTD April 7, 2024**\n\nLet $ABC$ be a triangle with $AB = 5, BC = 6, CA = 7.$ Let $D$ be a point on ray $AB$ beyond $B$ such that $BD = 7,$ $E$ be a point on ray $BC$ beyond $C$ such that $CE = 5,$ and $F$ be a point on ray $CA$ beyond $A$ such that $AF = 6.$ If the area of the circumcircle of $DEF$ can be written as $\\frac{a}{b} \\pi$ for relatively prime positive integers $a,b$, find $a+b$.", "description_html": "<p><strong>POTD April 7, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">ABC</span> be a triangle with <span class=\"katex--inline\">AB = 5, BC = 6, CA = 7.</span> Let <span class=\"katex--inline\">D</span> be a point on ray <span class=\"katex--inline\">AB</span> beyond <span class=\"katex--inline\">B</span> such that <span class=\"katex--inline\">BD = 7,</span> <span class=\"katex--inline\">E</span> be a point on ray <span class=\"katex--inline\">BC</span> beyond <span class=\"katex--inline\">C</span> such that <span class=\"katex--inline\">CE = 5,</span> and <span class=\"katex--inline\">F</span> be a point on ray <span class=\"katex--inline\">CA</span> beyond <span class=\"katex--inline\">A</span> such that <span class=\"katex--inline\">AF = 6.</span> If the area of the circumcircle of <span class=\"katex--inline\">DEF</span> can be written as <span class=\"katex--inline\">\\frac{a}{b} \\pi</span> for relatively prime positive integers <span class=\"katex--inline\">a,b</span>, find <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #120", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}