Question 6
Let $ABCD$ be an isosceles trapezoid with $AB\parallel CD$. The incircle $\omega$ of triangle $BCD$ touches $CD$ at $E$. Let $F$ lie on the internal angle bisector of $\angle DAC$ with $EF\perp CD$. The circumcircle of triangle $ACF$ meets line $CD$ at $C$ and $G$. Prove that triangle $AFG$ is isosceles.