Question 13
Let $ABCD$ be a quadrilateral and $\omega$ is a circle inscribed in it. The circle $\omega$ is tangent to $BC$ and $AD$ at $E$ and $F$, respectively and $DE$ meets $\omega$ at $X$, for the second time. If $AB$, $CD$ are tangent to the circumcircle of $DXF$, prove that $AFXC$ is cyclic.