εη₯¨ \( \qquad \)
In the xy-plane, ydrale has center. Cyrith coordinates \( (h, k) \). Points 4 and \( B \) lie \( y \) hothe circle. Point \( A^{\prime} \) has coordinates \( (h+1, k+\sqrt{102}) \), and \( \angle A C B \) is a right angle. What is the length of \( \overline{A B} \) ?
A) \( \sqrt{206} \)
\( 2 \sqrt{102} \)
C) \( 103 \sqrt{2} \)
D) \( 103 \sqrt{3} \)
\[
\begin{aligned}
d & =\sqrt{(h+1-h)^{2}+(\sqrt{102}-k)^{2}} \\
& =\sqrt{1^{2}+102-k^{2}} \\
d & =\sqrt{(h+1-h)^{2}+(k+\sqrt{102}-k)^{2}} \\
& =\sqrt{1^{2}+102} \\
& =\sqrt{103}
\end{aligned}
\]