# Circle A has a center at (3 ,7 ) and a radius of 1 . Circle B has a center at (-3 ,3 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

Distance between the two centres is $\sqrt{{\left(3 + 3\right)}^{2} + {\left(7 - 3\right)}^{2}}$
=$\sqrt{36 + 16} = \sqrt{52} = 7.211$ which is more than the sum of their radii =3. Hence the circles would not overlap and intersect. The smallest distance between the two circles would be along the line joining the two centres and it would be 7.211-(1+2)= 4.2111