None.
The Arctic Circle does not pass through any South American countries.
The Antarctic Circle does not pass through any countries.
There is no Atlantic Circle. The Antarctic Circle passes through no countries. See the related link for a map of the Antarctic Circle.
The Antarctic Circle doesn't pass through any countries at all.
The Antarctic Circle only passes through Antarctica.
None.
The Antarctic Circle passes through Antarctica, which is a continent with no countries.
None.
None.
The only country in the US that the Arctic Circle passes through is the US itself.
Siberia (part of Russia)
None. No states or countries either.