Let OABC be any planar quadrilateral. Let $G_1, G_2$ and $G_3$ be the centroids of OAB, OBC and OAC respectively, and let G be the centroid of the triangle $G_1G_2G_3$. Show that the points O, G and the centroid D of triangle ABC are collinear.
I have no idea how to start this any help would be appreciated
Take a coordinate system with its origin at $O$. From: $$ G_1 = \frac{O+A+B}{3},\qquad G_2=\frac{O+B+C}{3},\qquad G_3=\frac{O+A+C}{3}$$ we get: $$ \frac{G_1+G_2+G_3}{3} = \frac{2}{3}\cdot\frac{A+B+C}{3} $$ so $O$, the centroid of $G_1 G_2 G_3$ and the centroid of $ABC$ are collinear as wanted.