# Circle A has a center at #(5 ,4 )# and an area of #4 pi#. Circle B has a center at #(2 ,8 )# and an area of #9 pi#. Do the circles overlap? If not, what is the shortest distance between them?

##### 1 Answer

The circles *touch*, but they do not *overlap*. The shortest distance between them is

#### Explanation:

The distance between the points

If the circles overlap, the sum of their radii will be greater than

Let

Similarly,

We get

Since the sum of the radii matches the distance between the two circles' centers, the circles *touch*, but they do not *overlap*. The shortest distance between the two circles is