Geodesic
Metric properties of poncelet polygonal lines
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2012), pp. 43-47

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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. 
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     author = {E. A. Avksentyev},
     title = {Metric properties of poncelet polygonal lines},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {43--47},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_3_a8/}
}
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E. A. Avksentyev. Metric properties of poncelet polygonal lines. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2012), pp. 43-47. http://geodesic.mathdoc.fr/item/VMUMM_2012_3_a8/