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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