Let $O$ be the incenter of $\triangle{ABC}$. Connect $AO$, $BO$, and $CO$ and extends so that they intersect with $\triangle{ABC}$'s circumcircle at $D$, $E$, and $F$, respectively. Let $DE$ intersect $AC$ at $G$, and $DF$ intersects $AB$ at $H$. Show that $G$, $H$ and $O$ are collinear.