# Circle A has a center at (-9 ,-1 ) and a radius of 3 . Circle B has a center at (-8 ,3 ) and a radius of 1 . Do the circles overlap? If not what is the smallest distance between them?

The circles do not overlap.
Smallest distance between them$= \sqrt{17} - 4 = 0.1231$

#### Explanation:

From the given data:
Circle A has a center at (−9,−1) and a radius of 3 . Circle B has a center at (−8,3) and a radius of 1
. Do the circles overlap? If not what is the smallest distance between them?

Solution: Compute the distance from center of circle A to center of circle B.

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

$d = \sqrt{{\left(- 9 - - 8\right)}^{2} + {\left(- 1 - 3\right)}^{2}}$

$d = \sqrt{{\left(- 1\right)}^{2} + {\left(- 4\right)}^{2}}$

$d = \sqrt{1 + 16}$

$d = \sqrt{17}$

$d = 4.1231$

Compute the sum of the radii :

$S = {r}_{a} + {r}_{b} = 3 + 1 = 4$

Smallest distance between them$= \sqrt{17} - 4 = 0.1231$ God bless....I hope the explanation is useful.