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Miscellaneous triangle properties

Published online by Cambridge University Press:  23 January 2015

J. A. Scott
J. A. Scott*
Affiliation:
1 Shiptons Lane, Great Somerford, Chippenham SN15 5EJ
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Extract

In this note we will discuss five topics from triangle geometry and occasionally encounter something new. Areal coordinates (presented as Appendix A in [1]) will be used throughout, with the exception of the final section where it is advantageous to employ Cartesians.

The topics are:

(1) examples of collinearities where the distance ratios for important points vary with triangle shape;

(2) a pencil of lines which includes the Fermat, Napoleon and Vecten axes;

(3) two more circles related to the Lester circle;

(4) the family of rectangular hyperbolae which circumscribe the triangle of reference ABC and whose principal member is the Kiepert hyperbola [2];

(5) Cartesian coordinates leading to a solution of the ‘Euler disc problem’ [3].

Type
Articles
Information
The Mathematical Gazette , Volume 94 , Issue 529 , March 2010 , pp. 103 - 111
Copyright
Copyright © The Mathematical Association 2010

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References

1. Bradley, C. J., Challenges in geometry, Oxford (2005).CrossRefGoogle Scholar
2. Leversha, G. and Woodruff, P., From triangle to hyperbola, Math. Gaz. 86 (July 2002) pp. 311–316.CrossRefGoogle Scholar
3. Smith, G. and Leversha, G., Euler and triangle geometry, Math. Gaz. 91 (November 2007) pp. 436–452.Google Scholar
4. Kimberling, C., Triangle centres and central triangles, Congressum Numerantium, 129, Winnipeg (1998).Google Scholar
5. Fox, M. D. and Goggins, J. R., Cevian axes and related curves, Math. Gaz. 91 (March 2007) pp. 2–26.Google Scholar
6. Dolan, S., Man versus computer, Math. Gaz. 91 (November 2007) pp. 469–480.Google Scholar
7. Fox, M., A Euclidean proof of Aubel's theorem, Math. Gaz. 85 (July 2001) pp. 318–321.Google Scholar
8. Scott, J. A., A nine-point hyperbola, Math. Gaz. 89 (March 2005) pp.93–96.Google Scholar
9. Baker, H. F., Principles of geometry, CUP (1922) vol 2, p. 41.Google Scholar
10. Faulkner, T. E., Projective geometry, Oliver and Boyd (1952) p. 66.Google Scholar
11. Scott, J. A., Another rectangular hyperbola for the triangle, Math. Gaz. 92 (July 2008) pp. 331–332.CrossRefGoogle Scholar
12. Bradley, C. J., A theorem on concurrent Euler lines, Math. Gaz. 90 (November 2006) pp. 412–416.Google Scholar
13. Scott, J. A., A radical centre on the Euler line, Math. Gaz. 93 (July 2009) pp.312–314.Google Scholar