# 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?

Feb 17, 2016

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 $5 - \left(2 + 1\right) = 2$ units of the line joining the centers uncovered by either circle.