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A cyclic polygon has all its vertices of a polygon on a single circle, its circumcircle. Every nondegenerate triangle is a cyclic polygon, but a general quadrilateral is not: a convex quadrilateral is cyclic exactly when opposite interior angles sum to $\pi$. Every regular polygon is cyclic. For a side subtending central angle $\theta$, the chord length is $2R\sin (\theta /2)$, where $R$ is the circumradius; this converts placement on a circle into side-length calculations.