KöMaL 2016 B4789

The interior angle bisectors drawn from vertices $A$ and $B$ in a triangle $ABC$ intersect the circumscribed circle again at the points $G$ and $H$ , respectively. The points of tangency of the inscribed circle of triangle $ABC$ on sides $BC$ and $AC$ are $D$ and $E$ , respectively. Let $K$ denote the circumcentre of triangle $DCE$ . Show that the points $G$ , $H$ and $K$ are collinear.