Ans: C
Note that $\angle AOB = 135^\circ – 45^\circ = 90^\circ$. Therefore, $\Delta AOB$ is a right-angled triangle. Hence by the Pythagoras Theorem, we have
$\begin{array}{rcl}
AB^2 & = & 5^2 + 12^2 \\
AB & = & 13
\end{array}$
