# Circle A has a center at #(4 ,-8 )# and a radius of #3 #. Circle B has a center at #(-2 ,-2 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?

##### 1 Answer

No, since the distance of the centers is greater than the sum of the radii.

#### Explanation:

You can calculate the distance between the centers. If that distance is less than the sum of the radii, the circles do overlap. If not, they don't.

So, lets calculate the distance between

First we calculate the distance in x (called

You can see this as a triangle, with base

This shows us that the distance between the centers of the circles is approximately

Now we have a distance greater than