An Etude on One Sharygin's Problem
Boyan Zlatanov
TL;DR
This paper explores properties of geometric configurations derived from a complete quadrangle and a line using synthetic geometry, generalizing a classical problem with notable new theorems involving concurrency, collinearity, and conics.
Contribution
It introduces a generalized approach to a Sharygin problem, applying classical theorems to discover new geometric properties and configurations.
Findings
Identification of new concurrent lines
Discovery of collinear points
Emergence of conic sections in the configurations
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.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics