# Circle A has a center at (2 ,-1 ) and a radius of 4 . Circle B has a center at (-3 ,3 ) and a radius of 3 . Do the circles overlap? If not, what is the smallest distance between them?

Yes, the circles overlap

#### Explanation:

The distance between centers is
$d = \sqrt{{\left({x}_{b} - {x}_{a}\right)}^{2} + {\left({y}_{b} - {y}_{a}\right)}^{2}}$

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

d=sqrt((25+16)

$d = \sqrt{41} \cong 6.4 \text{ }$units

If they are tangent externally the distance between centers is

$d = 3 + 4 = 7 \text{ }$units

God bless....I hope the explanation is useful.