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 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-09T12:15:31

circles do not overlap

Minimum distance between circles A & B is #8.06 - 7 = color(red)(1.06)#

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#R_A = 3, O_A ((5),(9)), R_B = 4, O_B ((1),(2))#.

Center of circle B translated by #((3),(-1))#

Sum of radii #R_A + R_B = 3 + 4 = color(purple)(7)#

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

#vec(O_AO_B) = sqrt((5-4)^2 + (9-1)^2) = sqrt65 ~~ color(green)(8.06)#

#vec(O_AO_B) > R_A + R_B#

Hence the circles do not overlap

Minimum distance between circles A & B is #8.06 - 7 = color(red)(1.06)#