Alternate sides cyclic-2n-gons and Alternate angles circum-2n-gons

These polygons are respective generalizations of isosceles trapezia and kites, and defined by the following two dual results.

Alternate sides cyclic-2n-gons Alternate angles circum-2n-gons
A cyclic 2n-gon has n distinct pairs of adjacent angles equal, if and only if, a set of alternate sides are equal. A circumscribed 2n-gon has n distinct pairs of adjacent sides equal, if and only if, a set of alternate angles are equal.

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Alternate sides cyclic-2n-gons and Alternate angles circum-2n-gons

In the first figure, drag vertices A, B, D or F and in the second one, drag P, Q, R or S to dynamically change the figures.

Reference: De Villiers, M. (2011). Feedback: Equi-angular cyclic and equilateral circumscribed polygons. Mathematical Gazette, July, 95(533), p. 361.


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Michael de Villiers, 16 July 2011.