Question 196e8e6e

In the xy-plane, a circle has center $C$ with coordinates $\left(h,k\right)$. Points $A$ and $B$ lie on the circle. Point $A$ has coordinates $\left(h+1,k+\sqrt{102}\right)$, and $\angle ACB$ is a right angle. What is the length of $\overline{AB}$?