IR-MO-R2 2021 Problem 3

Circle $\omega$ is inscribed in quadrilateral $ABCD$ and is tangent to segments $BC, AD$ at $E,F$ , respectively. $DE$ intersects $\omega$ for the second time at $X$ . if the circumcircle of triangle $DFX$ is tangent to lines $AB$ and $CD$ , prove that quadrilateral $AFXC$ is cyclic.