About two characteristic points concerning two circles and their use in study of bicentric polygons

The article primarily deals with the connection between Fuss’ relation for bicentric n-gons where conics are two nested circles and Fuss’ relation for bicentric n-gons where conics are two separated circles. It is proved that one of them is quite determined by other. Also, the article deals with solutions of some old and difficult problems where characteristic points of two corresponding circles are defined and often used. Several interesting properties are established and some difficult problems are solved.