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

##### 1 Answer

The new centre of circle B will be

#### Explanation:

Translating circle B by

The radii of the circles are 2 and 3 respectively, so if their centres are now less than 5 units apart they will overlap, but if they are more than 5 units apart they will not.

To find the distance between the centres,

Because this is more than

graph{((x-3)^2+(y-5)^2-9)((x-7)^2+(y-3)^2-4)((x-2)^2+(y-2)^2-0.02)((x-3)^2+(y-5)^2-0.02)=0 [-6.04, 13.96, -1.44, 8.56]}