Question 168
Let $BL$ be an internal angle bisector in a scalene triangle $ABC$, with $L \in AC$. The extension of the median through $B$ meets the circumcircle $\omega$ of $ABC$ at point $D$. A line $\ell$ through the circumcenter of the triangle $BDL$ is parallel to $AC$. Prove that $\omega$ is tangent to $\ell$.