Question 1
Let $G$ be the centroid of triangle $ABC$ and $M$ the midpoint of $BC$. Let $X\in AB$, $Y\in AC$ such that $X,Y,G$ are collinear and $XY\parallel BC$. Suppose $XC$ and $GB$ intersect at $Q$, and $YB$ and $GC$ intersect at $P$. Show that triangle $MPQ$ is similar to triangle $ABC$.
