Problem
TxO Math Bowl 2024 - Individuals A - Problem 2
Consider a quadrilateral ABCD (vertices are in order) with \cos A = -\sin\left(90^\circ - C\right). 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.
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