The MathNet Korea
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

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. 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\$ Feuerbach, Kiepert, Jarabek, hyperbola, Orthology, antipedal triangle, complex numbers, homothetic 14Q05, 53A04, 14H45, 51N20