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

##### 1 Answer

Feb 8, 2016

The circles overlap.

#### Explanation:

To answer your question, let's compute the distance between the two centers

The distance can be computed due to Pythagorean theorem as follows:

#d = sqrt((3 - (-2))^2 + (1-1)^2) = sqrt(25 + 0) = 5#

As the first circle has a radius of

graph{((x-3)^2 + (y - 1)^2 - 36) * ((x+2)^2 + (y-1)^2 - 9) = 0 [-13.17, 15.31, -6.21, 8.03]}