Question 190
Let $ABC$ be an acute scalene triangle with centroid $G$. The rays $BG$ and $CG$ meet the circumcircle of $ABC$ again at points $P$ and $Q$. Let $D$ denote the foot of the altitude from $A$ to $BC$. Suppose ray $GD$ meets the circumcircle of $ABC$ again at $E$. Show that the circumcircle of triangle $ADE$ lies on line $PQ$.