# Circle A has a center at (-4 ,-2 ) and a radius of 4 . 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?

Dec 23, 2017

$\text{The circles do not overlap.}$
$\text{The smallest distance between them is "sqrt(50)-6" .}$

#### Explanation:

$\text{The distance between the two centers is }$
$\sqrt{{\left(- 4 - 1\right)}^{2} + {\left(- 2 - 3\right)}^{2}} = \sqrt{50} .$
$\text{The sum of the two radius is 6.}$
$\text{As "sqrt(50) > 6" the circles do not overlap.}$
$\text{The smallest distance between them is "sqrt(50) - 6" .}$