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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Glasnik Matematicki Serja III.
( Vol. 33 NO.2 / (1998))
Hyperbolas, Orthology, and Antipedal Triabgles
Zvonko Cerin,
Pages. 143-160
Abstract We obtain several characterisations of the Kiepert, Jarbek, and Feurbach
hyperbolas of a triangle $ABC$ using the antipedal triangles of a variable point
$P$ in the plane and the notion of orthologic triangles. Our arguments are
algebraic and use complex numbers.
Contents 1. Introduction
2. Preliminaries on complex numbers
3. Statements of results
4. Preliminaries for proofs
5. Proof of theorem 1 for $X=K$ and $i=1$
6. Proof of theorem 1 for $X=J$ and $i=1$
7. Proof of theorem 1 for $X=F$ and $i=1$
8. Proof of theorem 2 for $X=K, i=1$ and $j=5$
9. Proof of theorem 3 for $X=K$ and $i=1$
10. Proof of theorem 5 for $X=F$ and $i=e$
11. Proof of theorem 7
12. Outline of proof of theorem 8
13. Concluding remarks and an introduction to the appendix
14. Appendix-Preliminaries
15. Appendix-proof of theorem 4 for $X=K$ and $j=1$
16. Appendix-Proof of theorem 4 for $X=J$ and $j=2$
17. Appendix-Proof of theorem 4 for $X=F$ and $j=2$
18. Appendix-Proof of theorem 6 for $X=F, i=Oi, j'=1$ and $j=2$
Key words Feuerbach, Kiepert, Jarabek, hyperbola, Orthology, antipedal triangle, complex numbers, homothetic
Mathmatical Subject Classification 14Q05, 53A04, 14H45, 51N20