In triangle $ABC$ with centroid $G$, let $M \in (AB)$ and $N \in (AC)$ be points on two of its sides. Prove that points $M, G, N$ are collinear if and only if $\frac{MB}{MA}+\frac{NC}{NA}=1$.
Source: 2010 Saudi Arabia Pre-TST 1.4
Tags: geometry, Centroid, collinear
In triangle $ABC$ with centroid $G$, let $M \in (AB)$ and $N \in (AC)$ be points on two of its sides. Prove that points $M, G, N$ are collinear if and only if $\frac{MB}{MA}+\frac{NC}{NA}=1$.