TUYMAADA 2019 J7

A circle $\omega$ touches the sides $A$ B and $BC$ of a triangle $ABC$ and intersects its side $AC$ at $K$ . It is known that the tangent to $\omega$ at $K$ is symmetrical to the line $AC$ with respect to the line $BK$ . What can be the difference $AK -CK$ if $AB = 9$ and $BC = 11$ ?