Circle A has a radius of #3 # and a center of #(8 ,7 )#. Circle B has a radius of #2 # and a center of #(6 ,1 )#. If circle B is translated by #<2 ,7 >#, 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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Circles Overlap

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Given : #O_A ((8),(7)), R_A = 3, O_B ((6),(1)), R_B = 2#

#O_B# translated by #(2,7)#

New #O_B -> ((6+2),(1+7)) => ((8),(8))#

#vec(O_AO_B) = sqrt((8-8)^2 + (8-7)^2) = 1#

Sum of Radii #R_A + R_B = 3 + 2 = 5#

Since #R_A + R_B > vec(O_AO_B), both the circles overlap

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