Question 160
A point $D$ is chosen on side $BC$ of an acute triangle $ABC$ so that $AB = AD$. The circumcircle of triangle $ABD$ intersects segment $AC$ at points $A$ and $K$. Line $DK$ intersects the line perpendicular to $AC$ and passing through $B$ at point $L$. Prove that $CL = BC$. (I. Bogdanov)