Circle A has a radius of #5 # and a center of #(8 ,2 )#. Circle B has a radius of #3 # and a center of #(3 ,7 )#. If circle B is translated by #<2 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2016-09-30T20:02:20

The distance between the two centers is equal to the radius of the larger circle, therefore, the circles overlap

The new center of circle B is (5, 6)

The distance between the two centers is:

#d = sqrt((8 - 5)^2 + (2 - 6)^2)#

#d = sqrt(3^2 + (-4)^2)#

#d = sqrt(9 + 16)#

#d = 5#

The distance between the two centers is equal to the radius of the larger circle, therefore, the circles overlap