KöMaL 2020 B5107

The diagonals of a cyclic quadrilateral $ABCD$ intersect at $F$, the lines of sides $AB$ and $CD$ intersect at $E$, the midpoint of line segment $EF$ is $G$, the midpoint of line segment $BF$ is $H$, and the midpoint of side $BC$ is $I$. Show that $\angle GFD=\angle GIH$.