The distance around the outside of a circle is called the Circumference.
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I believe that the distance around a circle is called the circumference.
The distance around a circle is called circumference. Around any other shape, it is called perimeter.
Perimeter is the distance around something. In the case of a circle (or other curved figures), this is simply called the perimeter, so I would say perimeter is the same as circumference. Except that it is uncommon to call the circumference of a circle the "perimeter".
Concentric Circles?
We call it a circle.