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

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Answer 1 · 2018-02-09T10:12:05

Since #R_A + R_B < vec(O_AO_B)#, circles do NOT overlap

Minimum distance between the two circles A & B is #5.1 - 4 = color(red)(1.1#

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Given : #O_A (2,3), R_A = 1, O_B (6,4), R_B = 3#

#O_B# translated by (-3,4)

New coordinates of #O_B ((6-3),(4+4)) => ((3),(8))#

Now, #vec(O_AO_B) = sqrt((2-3)^2 + (3-8)^2) = sqrt26 ~~ 5.1#

Sum of radii #R_A + R_B = 1 + 3 = 4#

Since #R_A + R_B < vec(O_AO_B)#, circles do NOT overlap

Minimum distance between the two circles A & B is #5.1 - 4 = 1.1#