I have got a problem which I have to solve for my practive for an exam. Hope you can help me.
An isosceles trapezoid $ABCD$ with the parallel sides $\overline{AB}$ and $\overline{CD}$ is given. The incircle of $\triangle BCD$ touches $\overline{CD}$ in the point $P$. The line perpendicular to $\overline{CD}$ at $P$ meets the bisector of $\angle DAC$ at $F$. The circumcircle of $ \triangle ACF$ cuts $\overleftrightarrow{CD}$ at $C$ and $G$.
Show that $\triangle AFG$ is isosceles.
Thank you.