A porism concerning cyclic quadrilaterals

TL;DR

This paper proves a geometric porism about the existence of infinitely many cyclic quadrilaterals through four collinear points and introduces a matrix-based technique for such proofs, extending to quadrics.

Contribution

It presents a new geometric theorem on cyclic quadrilaterals and introduces a novel matrix method for proving such properties, generalizing to quadrics.

Findings

Existence of infinitely many cyclic quadrilaterals through four collinear points if one exists.

A matrix-based technique using pseudounitary traceless matrices for geometric proofs.

The property extends from circles to general quadrics.

Abstract

We present a geometric theorem on a porism about cyclic quadrilaterals, namely the existence of an infinite number of cyclic quadrilaterals through four fixed collinear points once one exists. Also, a technique of proving such properties with the use of pseudounitary traceless matrices is presented. A similar property holds for general quadrics as well as the circle.