Circle A has a radius of #2 # and a center of #(8 ,6 )#. Circle B has a radius of #4 # and a center of #(2 ,3 )#. If circle B is translated by #<-1 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2017-07-23T13:09:40

The circles do not overlap and the distance is #=1.07#

The coordinates of the center of circle #B'# after translation is

#C_B'=(2,3)+<-1,2> = (1,5)#

The distance between the centers is

#C_AC_B'=sqrt((1-8)^2+(5-6)^2)=sqrt(49+1)=sqrt50=7.07#

The sum of the radii is

#r_A+r_B=2+4=6#

As

#C_AC_B' > (r_A+r_B)#, the circles do not overlap

The shortest distance is #=7.07-6=1.07#

graph{((x-8)^2+(y-6)^2-4)((x-1)^2+(y-5)^2-16)=0 [-8.66, 16.65, -2.97, 9.69]}