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Jelly, 5 bytes

IA&lt;S}


Takes two complex numbers (centers) as first argument, and two real numbers (radii) as second argument.

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How it works

IA&lt;S}  Main link.
       Left argument:  [x1 + iy1, x2 + iy2]
       Right argument: [r1, r2]

I      Increments; yield (x2 - x1) + i(y2 - y1).
 A     Absolute value; yield √((x2 - x1)² + (y2 - y1)²).
   S}  Take the sum of the right argument, yielding r1 + r2.
  &lt;    Compare the results.