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

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Answer 1 · 2016-12-22T05:23:57

The circles do not overlap.
The smallest distance is #=2.1#

The distance between the centre is #d_c#

#sqrt((8-4)^2+(-4-3)^2)#

#=sqrt(16+49)=sqrt65#

The sum of the radii is #r_A+r_B#

#=4+2=6#

As #d_c>(r_A+r_B)#, the circles do not overlap.

The smallest distance between the cicles is

#=sqrt65-6=8.1-6=2.1#

graph{((x-8)^2+(y+4)^2-4)((x-4)^2+(y-3)^2-16)(y-3+7/4(x-4))=0 [-14.24, 14.24, -7.12, 7.12]}