Metric properties of poncelet polygonal lines

A generalization of the Radić-Kaliman theorem on metric relations in Poncelet polygonal curves is obtained in the papaer. A general principle for determination of condition for a closure of a Poncelet polygonal curve for two circles is derived from this result. In particular, explicit formulas for the inscribed-circumscribed $n$-gon for $n=5,6,8$ and an algorithm for finding such formulas for all $n$ are obtained.