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changed "diameter" to circumference, otherwise my suggestion doesn't make much sense :-)
elli
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you could try using a sewing needle or dressmaker's pin, repeatedly pricking the paper along the circumference of the circle. that would effectively result in a very closely perforated circle. then lightly press against the circle using some other blunt-tipped tool, and it should eventually "pop out".

elli
  • 41
  • 2