Question 22
$ABCD$ is a parallelogram such that $\angle ABC\lt 90^\circ$ and $\sin\angle ABC=\dfrac45$. The point $K$ is on the extension of $BC$ such that $DC=DK$; the point $L$ is on the extension of $DC$ such that $BC=BL$. The bisector of $\angle CDK$ intersects the bisector of $\angle LBC$ at $Q$. Suppose the circumradius of the triangle $ABD$ is $25$. Find the length of $KL$.