Geodesic
An elementary proof of Poncelet's theorem on bicentric polygons
Sbornik. Mathematics, Tome 209 (2018) no. 10, pp. 1533-1546

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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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     author = {A. M. Shelekhov},
     title = {An elementary proof of {Poncelet's} theorem on bicentric polygons},
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     number = {10},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_10_a5/}
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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/