# Circle A has a center at #(12 ,2 )# and an area of #13 pi#. Circle B has a center at #(3 ,6 )# and an area of #28 pi#. Do the circles overlap?

##### 1 Answer

We can find the radius of each circle given its area. If the centers are further apart than the sum of the two radii, the circles don't overlap. If not, they do. The radii are 3.6 and 5.3 units, totaling 8.9 units, and the distance between the centers is 9.85 units, so the circles **do not** overlap.

#### Explanation:

The area of a circle is given by

Circle A:

Circle B:

The sum of these two radii is

The distance between the centers is given by:

Since this is greater than the sum of the radii, the circles do not overlap.