Question 117
Side $BC$ of the parallelogram $ABCD$ is extended beyond the point $C$ and point $K$ is placed on the extension so that $\triangle CDK$ is isosceles triangle with base $CK$. Side $DC$ is extended beyond the point $C$ and point $L$ is placed on the extension so that $CBL$ is isosceles triangle with base $CL$. Bisectors of angles $\angle LBC$ and $\angle CDK$ intersect at point $Q$. Find radius of a circle circumscribed about triangle $ALK$, if $\angle BQD = \alpha$ and $KL = a$.