On The Ten Point Wood-Desargues' Configuration

TL;DR

This paper explores the geometric properties of the Wood-Desargues' configuration, revealing that certain centers form cyclic quadrangles with shared circumradius, extending understanding of this classical configuration.

Contribution

It demonstrates that the ten Hagge circle centers lie at vertices of five similar cyclic quadrangles with a common circumradius, adding new insights into the configuration.

Findings

Centers lie at vertices of five cyclic quadrangles

These quadrangles are similar to the initial configuration

The five quadrangles share a common circumradius

Abstract

The ten pairs of directly similar triangles in perspective in the Wood-Desargues' configuration have ten common Hagge circle centres. These centres are known to lie one each of the ten perspectrices. It is shown in this paper that these centres also lie at the vertices of five cyclic quadrangles, which are similar to the five cyclic quadrangles of the initial Wood-Desargues' configuration and that these five new cyclic quadrangles have a common circumradius.