English

An Etude on One Sharygin's Problem

History and Overview 2015-04-13 v1 Metric Geometry

Abstract

By the methods of the synthetic geometry we investigate properties of objects generated from a complete quadrangle and a line, which lies in its plane. We start with a problem from the book of Sharygin "Problems in Plane Geometry". We generalize this problem with the help of Pappus, Desargues and Pascal's Theorems and we discover new concurrent lines, collinear points, and conic sections.

Keywords

Cite

@article{arxiv.1405.3595,
  title  = {An Etude on One Sharygin's Problem},
  author = {Boyan Zlatanov},
  journal= {arXiv preprint arXiv:1405.3595},
  year   = {2015}
}

Comments

11 pages, 7 figures

R2 v1 2026-06-22T04:14:16.395Z