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The circumference of the small circle would be 18.84.
YES. A small circle is simply a circle around the earth that does not fly over the direct opposite place on earth that a plane took off from. A great circle goes full circumference of earth, where a small circle does not. Being a circle they both fly in a constant direction.
For the small circle of diameter 6, the circumference is 18.84.
radius of any circle = diameter/2
You can make your circle as large or as small as you want.