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

Answer 1

Circles are not overlapping. Smallest distance is 4.2111

Distance between the two centres is #sqrt((3+3)^2 +(7-3)^2)#

=#sqrt (36+16)= sqrt 52=7.211# which is more than the sum of their radii =3. Hence the circles would not overlap and intersect. The smallest distance between the two circles would be along the line joining the two centres and it would be 7.211-(1+2)= 4.2111

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Answer 2

Sadie Adams

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.