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

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Feb 9, 2018

Answer:

Circles A and B overlap.

Explanation:

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Circle A - #Center O_A (5,3), R_A = 4#

Circle A - #Center O_A (1,4), R_A = 3#

Circle B translated by (2,4)

New center of B #O_B ((1+2),(4+4)) => ((3),(8))#

#vec(O_A O_B) = sqrt((5-3)^2 + (3-8)^2) = sqrt29 ~~ 5.39#

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

Since #R_A + R_B > vec(O_A O_B)#, circles A and B overlap.

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