# Centroid Triangle

Geometry Level 2

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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