KöMaL 2018 B4954

Line $\ell$ passes through vertex $A$ of a triangle $ABC$, and it is parallel to $BC$. Let $\ell$ intersect the interior angle bisectors of angles $ABC$ and $ACB$ at $K$ and $L$, respectively. The inscribed circle touches $BC$ at point $D$. Show that the circumscribed circle intersects the Thales circle of line segment $KL$ at two points, and these two points are collinear with $D$.