Functions of triples of positive real numbers and their use in study of bicentric polygons

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Abstract

We consider some functions defined on the set of ordered triples $(R,r,d)$ , where $R,r,d>0$ and $R>r+d$ . The introduced properties of functions are used to study bicentric polygons where conics are circles. The article’s principal result is the so-called cyclical method for establishing Fuss’ relations for bicentric n-gons. The achieved method is a valuable contribution to the solution of the centuries-old Fuss’ relations problem.