Question

Circle A has a center at `(8 ,-4 )` and a radius of `3`. Circle B has a center at `(4 ,3 )` and a radius of `5`. 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 (approximately) `0.06` units

Explanation:

The centers of the circles at `(8,-4)` and `(4,3)` are separated by a distance of
`color(white)("XXX")sqrt((8-4)^2+(-4-3)^2)=sqrt(16+49)=sqrt(65)~~8.06`

Measured along the line segment joining the centers
`color(white)("XXX")`the radius of A uses up `3` units
and
`color(white)("XXX")`the radius of B uses up `5` units

which leaves
`color(white)("XXX")8.06 - (3+5) = 0.06` units along which the circles do not overlap.