Centroid Triangle

Geometry Level 3

Triangle \(ABC\) has centroid \(G\). Triangles \(ABG\), \(BCG\), and \(CAG\) have centroids \(G_1,G_2,G_3\) respectively.

The value of \(\dfrac{[G_1G_2G_3]}{[ABC]}\) can be represented by \(\dfrac{p}{q}\), for positive coprime integers \(p,q\).

Find \(p+q\).

\(\text{Details and Assumptions:}\)

\([ABCD]\) denotes the area of \(ABCD\).

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