Two Tangents, a Cyclic Quadrilateral, and a Perpendicular Median

A triangle configuration defined by two circumcircle tangents, a cyclicity condition, and a squared-side ratio determines a line perpendicular to a median. A complex-coordinate proof establishes existence, uniqueness, the prescribed point order, and the required perpendicularity.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23887894
Primary Topic
Mathematics and Applications
Type
preprint
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preprint

Two Tangents, a Cyclic Quadrilateral, and a Perpendicular Median

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

Two Tangents, a Cyclic Quadrilateral, and a Perpendicular Median

Ziping Guo
preprint en

Abstract

A triangle configuration defined by two circumcircle tangents, a cyclicity condition, and a squared-side ratio determines a line perpendicular to a median. A complex-coordinate proof establishes existence, uniqueness, the prescribed point order, and the required perpendicularity.

Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
DOIOpen Access PDFOpenAlex
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Two Tangents, a Cyclic Quadrilateral, and a Perpendicular Median — Ziping Guo · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS