Question

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

Answer 1

The circles do not overlap and are separated by a minimum distance of `2` units.

Explanation:

The length of the line segment joining the centers of the two circles is:
`color(white)("XXX")d=sqrt((3-(-1))^2+(-2-1)^2) =5`

Circle A covers `2` units of this line segment and
circle B covers `1` unit of this line segment,

leaving `5-(2+1)= 3` units of the line segment not covered by the circles.