CAPS 2000 Problem 5

Let $ABCD$ be an isosceles trapezoid with bases $AB$ and $CD$ . The incircle of the triangle $BCD$ touches $CD$ at $E$ . Point $F$ is chosen on the bisector of the angle $DAC$ such that the lines $EF$ and $CD$ are perpendicular. The circumcircle of the triangle $ACF$ intersects the line $CD$ again at $G$ . Prove that the triangle $AFG$ is isosceles.