Question 67
Let $ABC$ be a triangle. Line $\ell$ is parallel to $BC$ and it respectively intersects side $AB$ at point $D$, side $AC$ at point $E$, and the circumcircle of the triangle $ABC$ at points $F$ and $G$, where points $F, D, E, G$ lie in this order on $\ell$. The circumcircles of triangles $FEB$ and $DGC$ intersect at points $P$ and $Q$. Prove that points $A, P, Q$ are collinear.
(Slovakia)
(Slovakia)