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

##### 1 Answer

Jun 28, 2017

The circles do not overlap and the minimum distance is

#### Explanation:

Circle

The equation of circle

Circle

The equation of circle

The center of circle

Circle

The equation of the circle after translation is

The distance

This distance is greater than the sum of the radii

So, the circles do not overlap and the minimum distance is

graph{((x-2)^2+(y-7)^2-9)((x-6)^2+(y-1)^2-4)((x-8)^2+(y-8)^2-4)=0 [-7.28, 18.03, -1.57, 11.09]}