# Centroid Circle

Geometry Level 5

Let $$ABC$$ be a triangle, with $$AB=11$$ and $$AC=7$$, and let $$D,E,G$$ respectively be the midpoint of the side $$AC$$, the midpoint of $$AB$$ and the centroid of $$ABC$$. Knowing that $$A,D,E,G$$ are concyclic, and that $$BC=\sqrt{n}$$, find $$n$$.

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