Circle A has a center at #(8 ,3 )# and a radius of #3 #. Circle B has a center at #(-1 ,-2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?

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Answer 1 · 2016-11-08T18:56:04

They do not overlap. The closest distance between them is:

#sqrt(106) - 7 ~~ 3.3#

The distance, d, between the centers is:

#d = sqrt((8 - -1)^2 + (3 - -2)^2)#

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

#d = sqrt(106)#

This distance between the centers is greater than the sum of the radii, therefore, the circles do not overlap.

Here is a plot of the two circles:
enter image source here

The closest distance between them is:

#sqrt(106) - 7 ~~ 3.3#