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2005 AMC 10B Question 4

AMC10 · 2005 AMC 10B

Question 4

For real numbers $a$ and $b,$ define $a \diamond b = \sqrt{a^2 + b^2}.$ What is the value of $$
(5 \diamond 12) \diamond ((-12) \diamond (-5))?
$$
  1. $0$
  2. $\dfrac{17}{2}$
  3. $13$
  4. $13\sqrt{2}$
  5. $26$