KöMaL 2013 B4588

The point $D$ lies in the interior of a triangle ABC . Lines $CD$, $AD$ and $BD$intersect sides $AB$, $BC$ and $CA$ at the points $E$, $F$ and $G$, respectively. The intersection of lines $EG$ and $AF$ is $H$, and that of lines $EF$ and $BG$is $I$. Show that the lines $AB$, $FG$ and $HI$ are concurrent.