Problem

TxO Math Bowl 2024 - Individuals B - Problem 15

Let $\triangle ABC$ be a triangle with $AB = 7$ , $AC = 8$ , and $BC = 9$ with point $D$ on $AB$ and $E$ on $AC$ such that $BD = 3$ and $CE = 6$ . Let $O$ be the intersection of the perpendicular bisector of $DE$ with the angle bisector of $\angle A$ . Let $\omega$ be the circle centered at $O$ with radius $OD$ . Given that $F$ and $G$ are the two intersections of $\omega$ with $BC$ and $FG = N$ , find $N^4$ .

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Category: TxO Math Bowl Individual Round
Points: 7
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