Question 20
Let points $A$ and $B$ lie on circle $\omega$ with center $O$. Assume that $O$ does not lie on line $AB$. Let point $C$ lie on segment $AB$ and denote by $M$ and $N$ the midpoints of segments $AC$ and $CB$, respectively. The circumcircle of $AON$ intersects $\omega$ at $A$ and $K$ and the circumcircle of $BOM$ intersects $\omega$ at $B$ and $L$. Moreover, circumcircles of $AON$ and $BOM$ intersect each other at $O$ and $X$. Prove that the quadrilateral $CKXL$ is cyclic.