# Circle A has a center at (2 ,-1 ) and a radius of 3 . Circle B has a center at (-3 ,6 ) and a radius of 1 . Do the circles overlap? If not, what is the smallest distance between them?

Nov 7, 2016

They do not overlap. The shortest distance is $\sqrt{74} - 4 \approx 4.6$

#### Explanation:

Here is the graph of the circles:

The circles do not overlap.

The distance, d, between the centers is:

$d = \sqrt{{\left(2 - - 3\right)}^{2} + {\left(- 1 - 6\right)}^{2}}$

$d = \sqrt{{\left(5\right)}^{2} + {\left(- 7\right)}^{2}}$

$d = \sqrt{74}$

To find the shortest distance between them subtract the radii of both circles from d:

$\sqrt{74} - 4 \approx 4.6$