### Poncelet Theorem: What is it?

A Mathematical Droodle

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Two polygons with the same number of vertices inscribed into a fixed circle. Vertices of the polygons may be moved along the circle. Sides of the polygons are paired in such a way that paired sides always remain parallel. This is true if the number of vertices is even. If the number of vertices is odd, this is true for all but 1 pair of the sides. The two sides in the that special pair have equal lengths.

Let two n-gons be inscribed into the same circle. Assume that (n-1) sides of one polygon are successively parallel to (n-1) one sides of the second polygon. Then, the remaining two sides are parallel if n is even, and are equal if n is odd.

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