Circle A has a radius of #3 # and a center of #(2 ,7 )#. Circle B has a radius of #4 # 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?

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Answer 1 · 2018-02-09T09:53:41

Circles overlap .

Minimum distance between the circles is

Given : #A(2,7), R_A = 3#, #B (7,5), R_B = 4# B translated by (-1, 1)

Therefore, new coordinates of #B( (7-1), (5+1)) = B((6),(6))#

Distance between A and new B

#d = sqrt((2-6)^2 + (7-6)^2) = sqrt17 ~~ 4.123#

Circles overlap if# d < R_A + R_B# and NOT if #d> R_a + R_B#

#R_A + R_B = 3 + 4 = 7#

Since #d < R_A + R_B#, circles overlap