{"status": "success", "data": {"description_md": "\nLet $\\bigtriangleup ABC$ be an equilateral triangle, and let $O_1$ and $O_2$ be its circumcircle and incircle, respectively.\n\nIf the radius of the $O_1$ is $\\frac{\\sqrt{2}}{2}$ and the area inside $\\bigtriangleup ABC$ but outside $O_2$ is $\\frac{a\\sqrt{b}}{c}-\\frac{\\pi}{d}$, where $a$ and $c$ are relatively prime positive integers and $b$ is not divisible by the square of any prime, compute $a+b+c+d$.", "description_html": "<p>Let <span class=\"katex--inline\">\\bigtriangleup ABC</span> be an equilateral triangle, and let <span class=\"katex--inline\">O_1</span> and <span class=\"katex--inline\">O_2</span> be its circumcircle and incircle, respectively.</p>&#10;<p>If the radius of the <span class=\"katex--inline\">O_1</span> is <span class=\"katex--inline\">\\frac{\\sqrt{2}}{2}</span> and the area inside <span class=\"katex--inline\">\\bigtriangleup ABC</span> but outside <span class=\"katex--inline\">O_2</span> is <span class=\"katex--inline\">\\frac{a\\sqrt{b}}{c}-\\frac{\\pi}{d}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">c</span> are relatively prime positive integers and <span class=\"katex--inline\">b</span> is not divisible by the square of any prime, compute <span class=\"katex--inline\">a+b+c+d</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Christmas Contest - Team Round - Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p06", "prev": "/problem/christmas1_team-p04"}}