Question 46
In the triangle $ABC$ the point $M$ is the midpoint of $AB$, and the point $B'$ is the foot of the altitude from $B$ to $AC$. The circle ($CB'M$) intersects $BC$ again at $D$. The circles ($ABD$) and ($CB'M$) intersect again at $K$. The line parallel to $AB$ passing through $C$ intersects circle ($CB'M$) again at $L$. Prove that $KL$ bisects the segment $CM$.