Circle A has a radius of #2 # and a center of #(1 ,7 )#. Circle B has a radius of #2 # and a center of #(8 ,1 )#. If circle B is translated by #<-4 ,3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

1 Answer
CW
Sep 3, 2016

Circle A has a radius of 2 and a center of (1,7)
Circle B has a radius of 2 and a center of (8,1)
if circle B is translated by <-4,3>, the center will be (4,4)

Explanation:

distance bewteen circle A (1,7) and circle B (4,4) from center to center is
#=sqrt((4-1)^2+(4-7)^2) = sqrt(3^2+3^2)#
#=sqrt(9+9) = sqrt18 =sqrt(9xx2)#
#=3sqrt2 =4.24#
As circle A and Circle B each has a radius of 2, they do not overlap each other because 4.24 is greater than 2+2 =4 (the sum of the two radii)
the minimum distance between circle A and circle B is
#=4.24 -2 -2 = 0.24#

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