Question

Circle A has a center at `(2 ,2 )` and a radius of `5`. Circle B has a center at `(12 ,8 )` 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.
There is a minimum distance of `2sqrt(34)-6~~5.66` units between them.

Explanation:

The length of a line segment joining the centers of the two circles is
`color(white)("XXX")sqrt((12-2)^2+(8-2)^2) = sqrt(10^2+6^2) =2sqrt(34)`

The distance from the center of Circle A to the edge of Circle A along the line segment joining the two circles is `5` (the radius of A).

The distance from the edge of A to the center of Circle B along the line segment joining the centers is `2sqrt(34)-5`

The distance from the center of Circle B to the edge of Circle B along the line segment joining the centers is `1` (the radius of B).

The distance between the edges of the two circles is
`color(white)("XXX")(2sqrt(34)-5)-1`

`color(white)("XXX")=2sqrt(34)-6`

`color(white)("XXX")~~5.66` (in whatever nits are being used)