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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

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