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

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Answer 1 · 2016-06-23T02:22:11

Yes, the circles overlap

The distance between centers is
#d=sqrt((x_b-x_a)^2+(y_b-y_a)^2)#

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

#d=sqrt((25+16)#

#d=sqrt(41)~=6.4" "#units

If they are tangent externally the distance between centers is

#d=3+4=7" "#units

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