Circle A has a center at #(2 ,-1 )# and a radius of #3 #. Circle B has a center at #(-3 ,6 )# and a radius of #1 #. Do the circles overlap? If not, what is the smallest distance between them?

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Answer 1 · 2016-11-07T17:41:28

They do not overlap. The shortest distance is #sqrt(74) - 4 ~~ 4.6#

Here is the graph of the circles:
enter image source here

The circles do not overlap.

The distance, d, between the centers is:

#d = sqrt((2 - -3)^2+ (-1 - 6)^2)#

#d = sqrt((5)^2+ (-7)^2)#

#d = sqrt(74)#

To find the shortest distance between them subtract the radii of both circles from d:

#sqrt(74) - 4 ~~ 4.6#