Triangle PQR is drawn. Through it's vertices are lines drawn which are parallel to the opposite sides of the triangle. The new triangle formed is ABC. Prove that these two triangles have a common centroid.
I started by letting $M$ be the median of $[PQ]$, and then prove that bisector of $[BC]$ from $A$ occurs at $R$ while $M$ is collinear to $[AP]$. Firstly, I'm not sure whether or not this will suffice in proving they share a common centroid, and secondly I'm not sure where to start with the proof as setting up similar triangles from the parallel lines identity has lead to nothing.