{"status": "success", "data": {"description_md": "In $\\triangle ABC$, $$\\dfrac{\\cos{A}}{BC} = \\dfrac{\\cos{B}}{AC} = \\dfrac{\\cos{C}}{AB}.$$ Given that side $BC = 4$, then the area of $\\triangle ABC$ can be expressed as $a\\sqrt{b}$, where $a$ and $b$ are relatively prime positive integers and $b$ is not divisible by the square of any prime. Compute $a+b$.", "description_html": "<p>In <span class=\"katex--inline\">\\triangle ABC</span>, <span class=\"katex--display\">\\dfrac{\\cos{A}}{BC} = \\dfrac{\\cos{B}}{AC} = \\dfrac{\\cos{C}}{AB}.</span> Given that side <span class=\"katex--inline\">BC = 4</span>, then the area of <span class=\"katex--inline\">\\triangle ABC</span> can be expressed as <span class=\"katex--inline\">a\\sqrt{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</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</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Holiday Contest 2025 - Guts Round - Set 2 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}