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

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Answer 1 · 2016-10-10T18:25:13

The distance between the centers, #d~~ 6.3#, is less than the sum of their radii, #4 + 3 = 7#, therefore, the circles overlap.

The translation moves the center of the circle to the point #(3, 9)#.

Compute the distance between the centers:

#d = sqrt((5 - 3)^2 + (3 - 9)^2)#

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

#d = sqrt(4 + 36)#

#d = sqrt(40)#

#d~~ 6.3#

The distance between the centers, #d~~ 6.3#, is less than the sum of their radii, #4 + 3 = 7#, therefore, the circles overlap.