# Inspired by Centroid Circle: a problem by Emmanuel Lasker

Geometry Level 4

Let $$ABC$$ be a triangle, with $$AB=11$$ and let $$D,E,F,G$$ respectively be the midpoint of the side $$AC$$, the midpoint of $$AB$$,the midpoint of $$BC$$ and the centroid of $$ABC$$. Knowing that $$A,D,E,G$$ as well as $$B,E,G,F$$ are concyclic, and that $$BC=\sqrt{n}$$, Find $$\Sigma n$$ i.e. the sum of all possible values of $$n$$.

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