Successive Pedal Projections and a Nine-Point-Circle Criterion

Successive perpendicular projections associated with three incircle contact points give a criterion for a point of the incircle to lie on the nine-point circle. A rational parametrization and a Euclidean proof are supplied. Distinctness assumptions, contact-point exclusions, and the Feuerbach interpretation are stated explicitly.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23887910
Primary Topic
Mathematics and Applications
Type
preprint
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preprint

Successive Pedal Projections and a Nine-Point-Circle Criterion

Ziping Guo
Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
preprint

Successive Pedal Projections and a Nine-Point-Circle Criterion

Ziping Guo
preprint en

Abstract

Successive perpendicular projections associated with three incircle contact points give a criterion for a point of the incircle to lie on the nine-point circle. A rational parametrization and a Euclidean proof are supplied. Distinctness assumptions, contact-point exclusions, and the Feuerbach interpretation are stated explicitly.

Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
DOIOpen Access PDFOpenAlex
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Successive Pedal Projections and a Nine-Point-Circle Criterion — Ziping Guo · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS