Inscribed Polygons

A polygon is said to be inscribed in a circle if all its vertices are on the circumference of the circle.  Not every polygon can be inscribed in a circle.  For example, a parallelogram (which is not a rectangle) cannot be inscribed in a circle, because a circle containing three of its vertices cannot contain the fourth:

A polygon that can be inscribed in a circle is called a cyclic polygon.  For example, the following pentagon is cyclic:

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