Circle A has a radius of #2 # and a center of #(1 ,7 )#. Circle B has a radius of #6 # and a center of #(8 ,1 )#. If circle B is translated by #<-4 ,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

Answer:

Circles Overlap

Explanation:

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

Circle B translated by #((-4),(3))#

Sum of Radii #R_A + R_B = 2 + 6 = color(purple)(8#

New coordinates of #O_B -> ((8-4),(1+3)) => ((4),(4))#

#vec(O_AO_B) = sqrt((4-1)^2 + (4-7)^2) = sqrt18 ~~ color(green)(4.24#

Since sum of radii greater than the distance between the two circle

centers, Circles Overlap

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