\textbf{116.} The extensions of the asymptotes of the graph of the function $f(x) = \sqrt{x^2 + 2x} - \sqrt{x^2 - 2x}$, the first and third bisectors intersect at two points A and B. What is the length of AB?
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(1) $2\sqrt{7}$ \hspace{4cm} (2) $4$\\[6pt]
(3) $2\sqrt{5}$ \hspace{4cm} (4) $4\sqrt{7}$
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