I think what you're describing is the circumference.
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Diamitor means the legnth of the circle all around
Infinity
all the points in the inscribed circle are also in the bigger circle. If all the points in the outside circle are the set O ... and all the points in the inner circle are the set I... Then I is a subset of O, just like a venn diagram
If you are asking what the distance around a rectangle is called, the answer is "perimeter". that is not the question though is it???
Circumference is the outside of the circle and the inside is the are of the circle. And inside of the circle, there is diameter and radius. Radius is from the center point to the edge of the circle and diameter is all the way across.