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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)

Abstract

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.

Keywords

Brocard circle Brocard point Symmedian point 

References

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    Oxman, V., Sigler, A., Stupel, M.: On invariance of Brocard angles in interior and exterior Pappus triangles of any given triangle. J. Geom. Graph. 21(1), 61–70 (2017)MathSciNetzbMATHGoogle Scholar
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    Altshiller-Court, N.: College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle, 2nd edn., rev. enl. Barnes and Noble, New York (1952)Google Scholar
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    Weisstein, E.W.: Brocard Angle. From MathWorld—A Wolfram Web Resource http://mathworld.wolfram.com/BrocardAngle.html

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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