How many countries does the antarctic circle pass through

None

Explanation:

The Antarctic Circle, unlike the Arctic Circle, does not officially pass through any country. This is due in part to the lack of land masses at extreme southern latitudes, but also because no country can lay claim to Antarctic per the terms of the Antarctic Treaty.

On the Antarctic continent, the polar circle passes through territory claimed by France, Chile, Great Britain, Argentina and Australia, but none of these are official or recognized claims.