The Properties of Special Points on the Brocard Circle in a Triangle

  • Victor OxmanEmail author
  • Avi Sigler
  • Moshe Stupel
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)


In this paper we investigate some properties related to the Brocard circle of a given triangle ∆ABC. Four of them correspond to the special point of a triangle that satisfies some conditions. Another one corresponds to the special case of ∆ABC for which the relation \( ({\text{AC}}^{2} + {\text{AB}}^{2} )/2 = {\text{BC}}^{2} \) holds. We analyzed the case where a symmedian is a tangent to the Brocard circle. We found some interesting properties related to the Brocard circle for right angle triangle and for isosceles triangle.


Brocard circle Brocard point Symmedian point 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Shaanan CollegeHaifaIsrael
  2. 2.Western Galilee CollegeAcreIsrael
  3. 3.Technical College for Aviation ProfessionsHaifaIsrael
  4. 4.Gordon CollegeHaifaIsrael

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