Circle A has a radius of #5 # and a center of #(2 ,6 )#. Circle B has a radius of #2 # and a center of #(4 ,3 )#. If circle B is translated by #<-3 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

1 Answer
Jul 15, 2017

The circles overlap.

Explanation:

The new center of circle #B# is

#C'_B=(4,3)+<-3,1> =(1,4)#

The distance between the centers of the circles after translation is

#C_AC'_B=sqrt((1-2)^2+(4-6)^2)=sqrt(1+4)=sqrt5#

The sum of the radii is

#=r_A+r_B'=5+2=7#

As #C_AC_B'< r_A+r_B#, the circles overlap

graph{((x-2)^2+(y-6)^2-25)((x-1)^2+(y-4)^2-4)=0 [-10, 10, -5, 5]}