Question 13
A fixed circle $k$ is given, together with three collinear points $E$, $F$ and $G$ such that $E$ and $G$ lie outside the circle and $F$ lies inside the circle. Prove that if $ABCD$ is an arbitrary quadrangle, inscribed in the circle $k$ such that the extensions of the sides $AB$, $AD$ and $DC$ pass through $E$, $F$ and $G$ respectively, then its side $BC$ passes through a fixed point, collinear with $E$, $F$ and $G$, which doesn't depend on the quadrangle $ABCD$.