Problem 413

Given a triangle $\mathrm{ABC}$, where $2 \mathrm{BC}=\mathrm{AC}$ and angle $\mathrm{C}=78^{\circ}$. On the ray $\mathrm{BC}$, a segment $\mathrm{CK}=\mathrm{CB}$ is laid out. Then, from point $\mathrm{K}$, a perpendicular is drawn to the line containing the median of triangle $A B C$, drawn from vertex $\mathrm{B}$, and the intersection point is obtained as point L. What is the measure of angle CKL? Express your answer in degrees.