{"status": "success", "data": {"description_md": "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 $N^4$.", "description_html": "

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.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 7, "problem_name": "TxO Math Bowl 2024 - Individuals B - Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/txo2024indivsB-p14"}}