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NaturePaper

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I want to know whether it is correct that every convex polygon has an inner-circle (& hence an inner-radius). I think it is only possible for triangle and for regular polygon. Am I right?

If there is any convex N-gon having sides a_1,a_2,...,a_N which has an incircle, then what is the formula for the inner-radius in terms of the sides?

Regards,

NaturePaper