Circle A has a radius of #3 # and a center of #(5 ,9 )#. Circle B has a radius of #4 # and a center of #(1 ,2 )#. If circle B is translated by #<3 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-09T10:43:41

#R_A + R_B# #color(green)((7))# #># #vec(O_AO_B)# #color(blue)((4.123))#, the two circles A & B overlap.

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Circle A #O_A (5,9), R_A = 3#, Circle B #O_B (1,2), R_B = 4#

#O_B# #translated# #by# #(3,2)#

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

Distance #vec(O_AO_B) = sqrt((4-5)^2 + (5-9)^2) = sqrt17 ~~ 4.123#

Sum of radii #R_A + R_B = 3 + 4 = 7#

Since #R_A + R_B# #color(green)((7))# #># #vec(O_AO_B)# #color(blue)((4.123))#, the two circles A & B overlap.