Some inequalities in a triangle in which the length of one side and the inradius are given

• Victor Oxman ^[1]
  1. [1] Western Galilee College

     Western Galilee College

     Israel

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 53, Nº. 8, 2022, págs. 2226-2235
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In the article, we prove 18 inequalities involving inradius, a length of one side and one additional element of a given triangle. 14 of these inequalities are the necessary and sufficient conditions for the existence and uniqueness of such a triangle. All proofs are based on standard methods of calculus and can serve as a good demonstration of the relationship between different branches of mathematics (geometry, algebra, trigonometry, calculus). The article can be used by teachers and students in courses on advanced classical geometry.