# Circle A has a center at (1 ,7 ) and a radius of 3 . Circle B has a center at (-3 ,-2 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

Feb 2, 2016

they don't overlap. the smallest distance is 4.85

#### Explanation:

if the circles overlap,
the distance between the centers will be the sum of the two radius.

the distance between the two centers are,

$\sqrt{{\left(1 + 3\right)}^{2} + {\left(7 + 2\right)}^{2}}$

$= \sqrt{16 + 81}$

$= \sqrt{97}$

$= 9.85$

but the sum of the two circles are,

$3 + 2 = 5$

so, the circles don't overlap,

the smallest distance between the circles is,

$9.85 - 5 = 4.85$