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2017 AMC 12B Question 9

AMC12 · 2017 AMC 12B

Question 9

A circle has center $(-10, -4)$ and radius $13.$ Another circle has center $(3, 9)$ and radius $\sqrt{65}.$ The line passing through the two points of intersection of the two circles has equation $x + y = c.$ What is $c?$
  1. $3$
  2. $3\sqrt{3}$
  3. $4\sqrt{2}$
  4. $6$
  5. $\dfrac{13}{2}$