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The standings have been frozen.

It seems that examples in the statement are different from real test cases used in judge system.

Sorry.
Test case for Example 3 on judge system is different from the case written in the statement.

Judge system uses the following test case instead of Example 3.
---Input---
6 0 0
20 100 100

---Output---
25.104

what is the definition of regular polygon

It is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

If an edge of a polygon passes through another point, will it counted as a vertice?

No.

What languages can I use to request clarifications?

You can use only English. Please request clarifications with a message written in English.
英語で質問してください。
请用英语询问。