Circle A has a center at #(-2 ,-1 )# and a radius of #3 #. 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 · 2017-06-15T18:06:53

The circles touch one another without overlapping.

The distance between the centers is

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

#=sqrt(9+16)#

#=sqrt25=5#

The sum of the radii is

#r_A+r_B=3+2=5#

#d=r_A+r_B#

graph{((x+2)^2+(y+1)^2-9)((x-1)^2+(y-3)^2-4)=0 [-7.23, 5.26, -2.293, 3.947]}