{"status": "success", "data": {"description_md": "**POTD April 10, 2024**\n\nIsosceles triangles $ABC$ and $ABD$ have the same area. If $\\cot \\angle ACB=\\frac{2}{11}$, the smallest possible value of $\\cot \\angle BAD$ can be written as $-\\frac{a}{b}$ for relatively prime positive integers $a,b$. Find $a+b$.", "description_html": "<p><strong>POTD April 10, 2024</strong></p>&#10;<p>Isosceles triangles <span class=\"katex--inline\">ABC</span> and <span class=\"katex--inline\">ABD</span> have the same area. If <span class=\"katex--inline\">\\cot \\angle ACB=\\frac{2}{11}</span>, the smallest possible value of <span class=\"katex--inline\">\\cot \\angle BAD</span> can be written as <span class=\"katex--inline\">-\\frac{a}{b}</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": 3, "problem_name": "Problem of the Day #123", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}