# Circle A has a radius of #2 # and a center of #(3 ,7 )#. Circle B has a radius of #6 # and a center of #(8 ,1 )#. If circle B is translated by #<-4 ,3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

##### 1 Answer

The distance between the centers of the circle is less than the sum of the length of their radiuses. Thus the circles overlap and circle

#### Explanation:

**Given** : Circles A, B with centers and radiuses

**Required** :

If circle

Does

**Solution Strategy**:

a) Translate

b) Calculate the distance from

c) Is

If the above is

a) Translation Matrix of center vector

So the new center

b) Use the distance formula to calculate

c) Is Is

Since the distance from the center is less that the radius of