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Certain topics on polygons are extended from Euclidean to hyperbolicgeometry. This first part deals with uniqueness and existence of cocyclicpolygons with prescribed sidelengths. The non-Euclidean versions are moredifficult due to the existence of three different types of circles in thehyperbolic plane. The second part will be concerned with the problem ofmaximizing the area of polygons with fixed sidelengths. By the metric characterof these problems it is necessary to dispense to a certain extent withclassical hyperbolic trigonometry because angles must be replaced by lengthquantities. So this first part also takes regard of this technical aspect.

Polygons in hyperbolic geometry 1: Rigidity and inversion of the n-inequality