On One Locus in the Plane

  • Jiří BlažekEmail author
  • Pavel Pech
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)


In this work we deal with the problem: determine the locus of the point P such that the feet of the perpendiculars from P to (extended) sides of a given planar quadrilateral ABCD are concyclic. In general the locus is a cubic curve. We get a correspondence between some types of quadrilaterals and some classes of cubic curves. In the paper we answer several questions: For which quadrilaterals is the searched locus a cubic curve and for which a conic? What are properties of the cubic? For which quadrilaterals is the cubic decomposable? Which quadrilaterals correspond to singular cubic curves? What happens if a quadrilateral is tangential?


Locus Locus equation Cubic curves 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of South BohemiaCzech BudejoviceCzech Republic

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