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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