An inequality between the area of a triangle inscribed in a given triangle and the harmonic mean of the areas of vertex triangles

• Victor Oxman ^[1] ; Avi Sigler ^[2]
  1. [1] Western Galilee College

     Western Galilee College

     Israel

     
  2. [2] Shaanan College
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 52, Nº. 8, 2021, págs. 1253-1259
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof. The article can be used by teachers and students in courses on advanced classical geometry