Question

Circle A has a center at `(1 ,-2 )` and a radius of `2`. Circle B has a center at `(4 ,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.
There is a minimum distance of `2` units between them.

Explanation:

Distance between the centers of the circles:
`color(white)("XXX")d=sqrt((4-1)^2+(2-(-2))^2))=5`

The radius of A covers `2` units of the line joining the centers
The radius of B covers `1` unit of the line joining the centers.

This leaves `5-(2+1)=2` units of the line joining the centers uncovered by either circle.