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Rational Cyclic Polygons

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An cyclic polygon is called rational if it has rational area and the distance between any two of its vertices is also rational. In the general case, suppose three of the vertices have Cartesian coordinates

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,

,

.

Set , , . Then, for all , the coordinates of the remaining vertices () of the rational polygon are determined through the parameters by

.

This Demonstration shows , where .

Hover over a vertex to see its coordinates.

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Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA

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