{"status": "success", "data": {"description_md": "Consider a quadrilateral $ABCD$ (vertices are in order) with $\\cos{A}=-\\sin{(90^\\circ-C)}$. The diagonals of $ABCD$ intersect at point $I$. If $BI=6\\sqrt{6}$, $\\angle{CDB}=45^\\circ$, and $\\angle{ABD}=60^\\circ$, find the length of $AI$.", "description_html": "<p>Consider a quadrilateral <span class=\"katex--inline\">ABCD</span> (vertices are in order) with <span class=\"katex--inline\">\\cos{A}=-\\sin{(90^\\circ-C)}</span>. The diagonals of <span class=\"katex--inline\">ABCD</span> intersect at point <span class=\"katex--inline\">I</span>. If <span class=\"katex--inline\">BI=6\\sqrt{6}</span>, <span class=\"katex--inline\">\\angle{CDB}=45^\\circ</span>, and <span class=\"katex--inline\">\\angle{ABD}=60^\\circ</span>, find the length of <span class=\"katex--inline\">AI</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "TxO Math Bowl 2024 - Individuals A - Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024indivsA-p03", "prev": "/problem/txo2024indivsA-p01"}}