{"status": "success", "data": {"description_md": "Acute triangle $ABC$ has inradius $5$ and $AB < AC$. The foot of the altitude from $A$ to $BC$ intersects $BC$ at $P$, and $AP$ intersects the incircle at points $X$ and $Y$, with $AX<AY$. Given that $XY = 8$ and $BP=4$, the area of $ABC$ can be written as $\\frac{m}{n}$ for relatively prime positive integers $m$ and $n$. Compute $m+n$.", "description_html": "<p>Acute triangle <span class=\"katex--inline\">ABC</span> has inradius <span class=\"katex--inline\">5</span> and <span class=\"katex--inline\">AB &lt; AC</span>. The foot of the altitude from <span class=\"katex--inline\">A</span> to <span class=\"katex--inline\">BC</span> intersects <span class=\"katex--inline\">BC</span> at <span class=\"katex--inline\">P</span>, and <span class=\"katex--inline\">AP</span> intersects the incircle at points <span class=\"katex--inline\">X</span> and <span class=\"katex--inline\">Y</span>, with <span class=\"katex--inline\">AX&lt;AY</span>. Given that <span class=\"katex--inline\">XY = 8</span> and <span class=\"katex--inline\">BP=4</span>, the area of <span class=\"katex--inline\">ABC</span> can be written 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>. Compute <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Mock Euclid 2025 - Problem 8 Part A", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}