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 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2017-08-18T02:44:56

The distance between the centers of the circles is #sqrt2#, and since the radius of circle a is 5, the circles will definitely overlap.

The new center of circle B will be #(4-3,3+2)=(1,5)#.

We can now find the distance between the centres of the two circles:

#r = sqrt((x_a-x_b)^2+(y_a-y_b)^2)#

#= sqrt((x_a-x_b)^2+(y_a-y_b)^2)#

#= sqrt((2-1)^2+(6-5)^2)=sqrt2=1.414#

Given that the radius of circle a is 5, the circles will definitely overlap.