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

Abstract

For a given 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 $AC$.

19 pages, 8 figures