On the proof of Ptolemy's lemma
type: Item
instance of: scholarly article
title: On the proof of Ptolemy's lemma
zbMATH Open document ID: 1372.51012
DOI: 10.4171/EM/328
author: G. Wanner
author: Djura Paunić
published in: Elemente der Mathematik
publication date: 2017-07-27T00:00:00Z
review text: Ptolemy's lemma, stating that, in a cyclic quadrilateral with sides, in order, \(a,b,c,d\) and diagonals \(e\) and \(f\), one has (*) \(ac+bd=ef\), is proved by means of parallelogram area considerations. Given that (*) can be read as a statement regarding the sum of areas, the current proof can be considered to be more explanatory than Ptolemy's own, based on relations derived from some triangle similarity.
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 51M04
zbMATH DE Number: 6754351
zbMATH Keywords: Ptolemy's lemma
zbMATH Keywords: cyclic quadrilaterals
MaRDI profile type: Publication
Wikidata QID: Q124807090
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description: scientific article; zbMATH DE number 6754351