Geodesic
An elementary proof of Poncelet's theorem on bicentric polygons
Sbornik. Mathematics, Tome 209 (2018) no. 10, pp. 1533-1546 Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a new proof of Poncelet's theorem on bicentric polygons, using a generalisation of the notion of an orthocentre for an $n$-gon. We indicate some properties of bicentric polygons and find generalisations of Euler's formula connecting the radii of the inscribed and circumscribed circles and the distance between their centres for convex $n$-gons with $n=4, 5, 6$, and also for a non-convex pentagon. In conclusion, we consider a construction of three related bicentric pentagons. Bibliography: 6 titles.
Keywords: Poncelet's theorem on bicentric polygons
Mots-clés : orthocentre, Euler line. 
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A. M. Shelekhov. An elementary proof of Poncelet's theorem on bicentric polygons. Sbornik. Mathematics, Tome 209 (2018) no. 10, pp. 1533-1546. http://geodesic.mathdoc.fr/item/SM_2018_209_10_a5/

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