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

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Answer 1 · 2017-07-06T09:00:05

The circles do not overlap and the shortest distanceis #=3.07#

The distance between the centers is

#O_AO_B=sqrt((1-(-4))^2+(3-(-2))^2)#

#=sqrt(25+25)#

#=sqrt50=7.07#

The sum of the radii is

#r_A+r_B=2+2=4#

As,

#O_AO_B> (r_A+r_B)#

The circles do not overlap.

The smallest distance is

#d=7.07-4=3.07#

graph{((x+4)^2+(y+2)^2-4)((x-1)^2+(y-3)^2-4)(y-3-x+1)=0 [-10, 10, -5, 5]}