Circle A has a center at #(1 ,7 )# and a radius of #3 #. Circle B has a center at #(-3 ,-2 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?

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Answer 1 · 2016-02-02T11:48:45

they don't overlap. the smallest distance is 4.85

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if the circles overlap,
the distance between the centers will be the sum of the two radius.

the distance between the two centers are,

#sqrt((1+3)^2+(7+2)^2)#

#=sqrt(16+81)#

#=sqrt(97)#

#=9.85#

but the sum of the two circles are,

#3+2=5#

so, the circles don't overlap,

the smallest distance between the circles is,

#9.85-5=4.85#