{"status": "success", "data": {"description_md": "**POTD January 26, 2024**\n\nConsider triangle $ABC$ with $AB=AC$. Given that the orthocentre $H$ lies on the incircle $\\omega$ and $\\cos(\\angle A)$ can be expressed as $\\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, find the value of $m+n$.", "description_html": "<p><strong>POTD January 26, 2024</strong></p>&#10;<p>Consider triangle <span class=\"katex--inline\">ABC</span> with <span class=\"katex--inline\">AB=AC</span>. Given that the orthocentre <span class=\"katex--inline\">H</span> lies on the incircle <span class=\"katex--inline\">\\omega</span> and <span class=\"katex--inline\">\\cos(\\angle A)</span> can be expressed as <span class=\"katex--inline\">\\frac{m}{n}</span> for relatively prime positive integers <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span>, find the value of <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #52", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}