# Circle A has a radius of #2 # and a center of #(2 ,7 )#. Circle B has a radius of #6 # and a center of #(7 ,5 )#. If circle B is translated by #<-1 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

##### 1 Answer

circle B do not overlap.

Shortest distance is

#### Explanation:

Circle A

Center

radius

Equation of circle A

Circle B

Center

radius

Equation of circle B

ranslation of B

<-1,1>

Center of B after translation

Center of B after translation

Equation of circle B after translation

Intersection of the circles

and

can be found out

Distance from center of Circle A to

center of Circle B is

Radius of circle A is

point on the Perimeter of the circle B is away from its center by 6

point on the Perimeter of the circle B is away from (2,7) is

Hence, the two circles donot overlap.

Shortest distance is