For real numbers $a$ and $b$, define $a \diamond b = \sqrt{a^2 + b^2}$. What is the value of
$(5 \diamond 12) \diamond ((-12) \diamond (-5))$?
$\textbf{(A) } 0 \qquad \textbf{(B) } \frac{17}{2} \qquad \textbf{(C) } 13 \qquad \textbf{(D) } 13\sqrt{2} \qquad \textbf{(E) } 26$
\begin{align*} (5 \diamond 12) \diamond ((-12) \diamond (-5))&=(\sqrt{5^2+12^2}) \diamond (\sqrt{(-12)^2+(-5)^2})\\ &=(\sqrt{169})\diamond(\sqrt{169})\\ &=13\diamond13\\  &=\sqrt{13^2+13^2}\\  &=\sqrt{338}\\  &=\boxed{\mathrm{(D)\,13\sqrt{2}}}\\ \end{align*}
Note that the negative signs did not matter and any number squared times two is that number times the square root of 2.