Analogous properties are valid for circumscriptible polygons with an even number of sides. For such polygons the corresponding arc-polygon p1, closes after visiting each side once and not two times as in the odd-number of sides case. Thus, the resulting arc-polygon p1 has equal number of vertices with the original polygon. An example, for a circumscriptible hexagon and suggestions for the proofs are given in SuccessiveArcsHex.html .

The subject is related to the composition of rotations about the vertices of a polygon. The vertices of the arc-polygon p1 constitute an orbit of the group generated by these rotations. Look at the file RotationsOnQuadrangleVertices.html , for a discussion of these matters.

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