Problem

TxO Math Bowl 2024 - Team Contest - Problem 14

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 $p + q$ .

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Category: TxO Math Bowl Team Contest
Points: 5
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