Metric properties of Poncelet polygonal curves / *E. A. Avksent'ev.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 3. P. 43-47
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

A generalization of the Radic-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*n=5,6,8 and an algorithm for finding such formulas for all *n* are obtained.

*Key words*:
Poncelet theorem, inscribed-circumscribed $n$-gon, pencil of circles, closure theorems, closure conditions.