Centroid Triangle

Geometry Level 2

Triangle ABCABC has centroid GG. Triangles ABGABG, BCGBCG, and CAGCAG have centroids G1,G2,G3G_1,G_2,G_3 respectively.

The value of [G1G2G3][ABC]\dfrac{[G_1G_2G_3]}{[ABC]} can be represented by pq\dfrac{p}{q}, for positive coprime integers p,qp,q.

Find p+qp+q.

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

[ABCD][ABCD] denotes the area of ABCDABCD.

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