Centroid Circle

Geometry Level 5

Let ABCABC be a triangle, with AB=11AB=11 and AC=7AC=7, and let D,E,GD,E,G respectively be the midpoint of the side ACAC, the midpoint of ABAB and the centroid of ABCABC. Knowing that A,D,E,GA,D,E,G are concyclic, and that BC=nBC=\sqrt{n}, find nn.

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