# Circle A has a radius of #3 # and a center of #(5 ,4 )#. Circle B has a radius of #4 # and a center of #(7 ,2 )#. If circle B is translated by #<3 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

##### 1 Answer

Jul 6, 2017

The circles overlap

#### Explanation:

Let the center of the circle

and the center of the circle

The center after translation is

The distance between the centers is

The sum of the radii is

As ,

The circles overlap

graph{((x-5)^2+(y-4)^2-9)((x-7)^2+(y-2)^2-16)((x-10)^2+(y-4)^2-16)=0 [-6, 16.5, -2.185, 9.065]}