Question

Circle A has a center at `(3 ,7 )` and a radius of `2`. Circle B has a center at `(4 ,-1 )` and a radius of `6`. 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 (approximately) `0.06` between them

Explanation:

The distance between the centers of A and B is
`color(white)("XXX")sqrt((3-4)^2+(7-(-0))^2) = sqrt(65) ~~8.06`

Considering the line segment which joins the two centers
`color(white)("XXX")`Circle A covers 2 units of this line segment
`color(white)("XXX")`Circle B covers 6 units of this line segment.

Together the two circles cover `(2+6)=8` units of the line segment which is `8.06` long; leaving a distance of `0.06` between the two circles.