Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image>Chords $\overline{JF}$ and $\overline{BC}$ intersect at $K .$ If $B K=8$, $K C=12,$ and $K F=16,$ find $J K$