# Circle A has a center at #(3 ,5 )# and a radius of #1 #. Circle B has a center at #(-1 ,1 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?

##### 1 Answer

Feb 2, 2016

The circles do **not** overlap.

The minimum distance between them is

#### Explanation:

The distance between the centers of the two circles is

Consider a line segment joining the two centers.

The distance from A's center to A's circumference is

The distance from B's center to B's circumference is

The sum of the radial distances is

by