Relations among five radii of circles in a triangle, its sides and other segments

• Avi Sigler ^[2] ; Moshe Stupel ^[2] ; Alfinio Flores ^[1]
  1. [1] University of Delaware

     University of Delaware

     Estados Unidos

     
  2. [2] Shaanan Academic Religious Teachers College
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 48, Nº. 5, 2017, págs. 782-793
• Idioma: inglés
• DOI: 10.1080/0020739x.2016.1276227
• Texto completo no disponible (Saber más ...)
• Resumen

  • Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas relating the radii to the sides and the inequalities between the different averages. The activities described were conducted with pre-service teachers of mathematics, with empirical investigation of the relations using dynamical geometry software, and formal presentation of proofs.