Question 3
Let $G$ be an interior point of triangle $ABC$. Let $M,N,P$ be the intersections of $AG,BG,CG$ with sides $BC,CA,AB$, respectively. Suppose $\dfrac{AG}{GM}+\dfrac{BG}{GN}+\dfrac{CG}{GP}=6$. Prove that $G$ is the centroid of triangle $ABC$.
