About a sequence of points and a relationship between pencils of conics and circles in the Euclidean plane

2021/10/07 by Živadinović, Andrija, Toljić, Veljko
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.03597

Abstract

For a given triangle \triangle ABC, we define two sequences of points on line BC and provide their generalizations to real functions such that centers of circumscribed circles around A and adjacent points in subsequences generate a pencil of conics touching perpendicular bisectors of AB and AC.

Related

• Bisector fields and pencils of conics
• Triangle conics and cubics
• Bisector fields of quadrilaterals
• The conic geometry of rectangles inscribed in lines
• Miquel circles and Cevian lines