Proving concurrency by loci

Saeed Salehi ^[1]
1. [1] University of Tabriz
  
  University of Tabriz
  
  Irán
Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 56, Nº. 4, 2025, págs. 800-808
Idioma: inglés
DOI: 10.1080/0020739X.2023.2279753
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Resumen
- A fascinating and catchy method for proving that a number of special lines concur is using the concept of locus. This is now the classical method for proving the concurrency of the internal angle bisectors and perpendicular side bisectors of a triangle. In this paper, we prove the concurrency of the altitudes and the medians by showing that they are loci of some interesting points. Our proofs for these ancient theorems seem to be new. We also provide loci method proofs for the concurrency theorems of Ceva and Carnot.