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. 67, N 3, 2012.].

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 nn=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.