{"status": "success", "data": {"description_md": "In cyclic quadrilateral $ABCD$, we have $AB=AD$ and $AC=BC$. Denote the incenter of $\\triangle ABC$ as $I$. Suppose that $I$ lies on $\\overline{BD}$ and that $AI = 24$. Then, $BC$ can be expressed as $p+\\sqrt{q}$ where $p$ and $q$ are positive integers. Compute $p+q$.", "description_html": "<p>In cyclic quadrilateral <span class=\"katex--inline\">ABCD</span>, we have <span class=\"katex--inline\">AB=AD</span> and <span class=\"katex--inline\">AC=BC</span>. Denote the incenter of <span class=\"katex--inline\">\\triangle ABC</span> as <span class=\"katex--inline\">I</span>. Suppose that <span class=\"katex--inline\">I</span> lies on <span class=\"katex--inline\">\\overline{BD}</span> and that <span class=\"katex--inline\">AI = 24</span>. Then, <span class=\"katex--inline\">BC</span> can be expressed as <span class=\"katex--inline\">p+\\sqrt{q}</span> where <span class=\"katex--inline\">p</span> and <span class=\"katex--inline\">q</span> are positive integers. Compute <span class=\"katex--inline\">p+q</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024team-p15", "prev": "/problem/txo2024team-p13"}}