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

Jun 15, 2017

The circles touch one another without overlapping.

#### Explanation:

The distance between the centers is

$d = \sqrt{{\left(- 2 - 1\right)}^{2} + {\left(- 1 - 3\right)}^{2}}$

$= \sqrt{9 + 16}$

$= \sqrt{25} = 5$

The sum of the radii is

${r}_{A} + {r}_{B} = 3 + 2 = 5$

$d = {r}_{A} + {r}_{B}$

graph{((x+2)^2+(y+1)^2-9)((x-1)^2+(y-3)^2-4)=0 [-7.23, 5.26, -2.293, 3.947]}