An elementary proof of Poncelet's theorem on bicentric polygons. (October 2018)

• Record Type: Journal Article
• Authors: Shelekhov, A. M.
• Is Part Of: Sbornik. Volume 209:Number 10(2018)
• Page Start: 1533
• Page End: 1546
• Publication Date: 2018-10
• Subjects: 51M04; 51N20; Poncelet's theorem on bicentric polygons -- orthocentre -- Euler line; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM8979
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: We give a new proof of Poncelet's theorem on bicentric polygons, using a generalisation of the notion of an orthocentre for an -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 -gons with, and also for a non-convex pentagon. In conclusion, we consider a construction of three related bicentric pentagons. Bibliography: 6 titles.