# Circle A has a center at (7 ,-2 ) and a radius of 1 . Circle B has a center at (4 ,2 ) and a radius of 4 . Do the circles overlap? If not, what is the smallest distance between them?

Nov 4, 2016

The circles are tangent to each other at one and only one point, therefore, the smallest distance between them is zero.

#### Explanation:

Let d = the distance between the centers

$d = \sqrt{{\left(7 - 4\right)}^{2} + {\left(- 2 - 2\right)}^{2}}$

$d = \sqrt{9 + 16}$

$d = 5$

This is the sum of the radii, therefore, the circles are tangent to each other at one and only one point.