# Brazilian Contest - Geometry

Geometry Level pending

Let $$N$$ be the point of the side $$AC$$ of the triangle $$ABC$$ such that $$AN = 2NC$$ and the $$M$$ point of the side AB such that $$MN$$ perpendicular to $$AB$$. Knowing $$AC = 12$$cm and that centroid $$G$$ of triangle $$ABC$$ belongs to the $$MN$$ segment.

Determine the length of $$BG$$ segment.

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