Circle A has a radius of #4 # and a center of #(7 ,3 )#. Circle B has a radius of #2 # and a center of #(2 ,2 )#. If circle B is translated by #<1 ,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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circles overlap

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#O_A ((7),(3)), R_A = 4, O_B ((2),(2)), R_B = 2#

#O_B translated by ((1),(3))#

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

#vec(O_AO_B) = sqrt((7-3)^2 + (3-5)^2) = sqrt20 ~~ 4.47#

Sum of Radii #R_A + R_B = 4 + 2 = 6#

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

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