Circle A has a radius of #2 # and a center of #(3 ,1 )#. Circle B has a radius of #6 # and a center of #(8 ,5 )#. 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?

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Feb 9, 2018

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Since #color(blue)(R_A + R_B (8)) color(green)(>) color(red)(vec(O_AO_B) (5.83)# circles A & B overlap

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#O_A ((3),(1)), R_A = 2#, #O_B ((8), (5)), R_B = 6#

#O_B# translated by (-4,3)

New #O_B = ((3-5),(1+3)) => ((-2),(4))#

#vec(O_AO_B) = sqr((-2-3)^2 + (4-1)^2) = sqrt34 ~~ 5.83#

Sum of radii #R_A + R_B = 2 + 8 = 8#

Since #R_A + R_B (8) > vec(O_AO_B) (5.83)# the circles overlap

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