# Circle A has a center at (-1 ,1 ) and a radius of 2 . Circle B has a center at (3 ,-2 ) and a radius of 1 . Do the circles overlap? If not what is the smallest distance between them?

Feb 24, 2016

The circles do not overlap and are separated by a minimum distance of $2$ units.

#### Explanation:

The length of the line segment joining the centers of the two circles is:
$\textcolor{w h i t e}{\text{XXX}} d = \sqrt{{\left(3 - \left(- 1\right)\right)}^{2} + {\left(- 2 - 1\right)}^{2}} = 5$

Circle A covers $2$ units of this line segment and
circle B covers $1$ unit of this line segment,

leaving $5 - \left(2 + 1\right) = 3$ units of the line segment not covered by the circles.