Question 150
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
$$
\frac{MB}{MA} + \frac{NC}{NA} = 1
$$
$$
\frac{MB}{MA} + \frac{NC}{NA} = 1
$$