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

Sep 9, 2016

No, they do not overlap. See the explanation and graph below.
The smallest distance between them =0.71.

#### Explanation:

Circle A, center (-4,2), r=3
Circle B, center (2,-1), r=3

the sum of the two radii = 3+3 =6

the distance between the two center points
$= \sqrt{{\left(- 1 - 2\right)}^{2} + {\left(2 + 4\right)}^{2}} = \sqrt{{3}^{2} + {6}^{2}} = \sqrt{45} = 6.71$

As the distance between the two center points is bigger than the sum of the two radii, the circles do not overlap.

The smallest distance between them $6.71 - 3 - 3 = 0.71$

The yellow line linking the two center points is 6.71 in length, which is greater than the sum of the two radii. So the two circles do not overlap.