Question

Circle A has a center at `(3 ,5 )` and a radius of `1`. Circle B has a center at `(-1 ,1 )` and a radius of `4`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

The circles do not overlap.
The minimum distance between them is `4sqrt(2)-5 ~~0.66`

Explanation:

The distance between the centers of the two circles is
`color(white)("XXX")sqrt((3-(-1))^2+(5-1)^2) = 4sqrt(2) ~~5.66`

Consider a line segment joining the two centers.
The distance from A's center to A's circumference is `1`.
The distance from B's center to B's circumference is `4`.
The sum of the radial distances is `1+4=5` which is less than the length of the line segment `4sqrt(2)~~5.66`
by `5.66-5=0.66` (units).