Around the Carnot theorem

TL;DR

This paper explores the Carnot theorem and related geometric configurations, proving new properties about points, lines, and conics, and confirming an open conjecture using classical theorems.

Contribution

It provides new proofs and insights into the geometric configurations associated with Carnot's theorem, including an equivalent statement and an open conjecture.

Findings

Certain points lie on the same lines and conics

An equivalent statement to Carnot's theorem is proven

An open conjecture by Bradley is confirmed

Abstract

We study the Carnot theorem and the configuration of points and lines in connection with it. It is proven that certain significant points in the configuration lie on the same lines and same conics. The proof of an equivalent statement formulated by Bradley is given. An open conjecture, established by Bradley, is proved using the theorems of Carnot and Menelaus.