Question 95
Let $ABC$ be a triangle and $G$ its centroid. Let $G_{a}$, $G_{b}$ and $G_{c}$ be the orthogonal projections of $G$ on sides $BC$, $CA$, respectively $AB$. If $S_{a}$, $S_{b}$ and $S_{c}$ are the symmetrical points of $G_{a}$, $G_{b}$, respectively $G_{c}$ with respect to $G$, prove that $AS_{a}$, $BS_{b}$ and $CS_{c}$ are concurrent.