# Circle A has a radius of #2 # and a center at #(3 ,1 )#. Circle B has a radius of #4 # and a center at #(8 ,3 )#. If circle B is translated by #<-4 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

##### 1 Answer

Jan 13, 2018

They don't overlap. The minimum distance is

#### Explanation:

The new center of circle B is

The distance between the centers of the two circles is

Circle B is the larger circle and all points on the circle are 4 units from its center.

The radius of circle A is 2 and the center of A is

The minimum distance between points on A and B is actually the radius of B, which is 4, minus the farthest any point on A can be from the center of B, which is