Cyclic polygons in classical geometry (Q2844625)

A cyclic polygon is a polygon whose vertexes are on a same circle. The authors show that the same relationships about the side lengths, diagonal lengths and the radius of the circumcircle hold in Euclidean, hyperbolic and spherical geometry. More precisely, starting from different theorems about cyclic polygons in Euclidean geometry, the authors provide a machinery to generate similar theorems in the hyperbolic or in the spherical geometry.