# Circle A has a center at (-5 ,7 ) and a radius of 4 . Circle B has a center at (7 ,2 ) and a radius of 3 . Do the circles overlap? If not, what is the smallest distance between them?

The circles do not overlap and the shortest distance between them is $6$ units.
$\sqrt{{\left(- 5 - 7\right)}^{2} + {\left(7 - 2\right)}^{2}} = 13 > 7 = 3 + 4$
The distance between the center of the 2 circles is larger than the sum of the 2 radii of the circles, hence the circles do not overlap, and the shortest distance between them is $13 - 7 = 6$ units.