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Math·Geometry and Trigonometry·Circles

hard

In the xy-plane, a circle has center $C$ with coordinates $(h,k)$. Points $A$ and $B$ lie on the circle. Point $A$ has coordinates $(h+1,k+\sqrt{230})$, and $\angle ACB$ is a right angle. What is the length of $\overline{AB}$?

A

$231\sqrt{3}$

B

$231\sqrt{2}$

C

$2\sqrt{230}$

D

$\sqrt{462}$