Vol. 23 No. 2 (2025)

Articles

On the nine-point conic of hyperbolic triangles

Published:

2025-12-01

https://doi.org/10.5485/TMCS.2025.15646

Author

Zoltán Szilasi

Institute of Mathematics, University of Debrecen, Hungary

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Keywords

Cayley-Klein plane hyperbolic triangles Feuerbach circle eleven-point conic

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Copyright (c) 2025 Zoltán Szilasi

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Selected Style: APA

Szilasi, Z. (2025). On the nine-point conic of hyperbolic triangles. Teaching Mathematics and Computer Science, 23(2), 195-211. https://doi.org/10.5485/TMCS.2025.15646

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Abstract

In the Cayley–Klein model, we review some basic results concerning the geometry of hyperbolic triangles. We introduce a new definition of the circumcircle of a hyperbolic triangle, guaranteed to exist in every case, and describe its main properties. Our central theorem establishes, by means of purely elementary projective geometric arguments, that a hyperbolic triangle has a nine-point conic if and only if it is a right triangle.

Subject Classification: 51M09

References

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