Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-12T13:49:05.614Z Has data issue: false hasContentIssue false
  • English
  • Français

Hagge circles and isogonal conjugation

Published online by Cambridge University Press:  01 August 2016

Christopher Bradley  and
Geoff Smith
Christopher Bradley
Affiliation:
6A Northcote Road, Clifton, Bristol BS8 3HB
Geoff Smith
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

Let Q be a point on the circumcircle of triangle ABC. The reflections of Q in the three triangle sides are known to be collinear, and the line thus defined contains the orthocentre H. This fact can form the basis of a proof of the existence of the Simson line, or alternatively can be deduced from the existence of the Simson line by enlarging the Simson line by a factor of 2 from the centre Q.

Type
Articles
Information
The Mathematical Gazette , Volume 91 , Issue 521 , July 2007 , pp. 202 - 207
Copyright
Copyright © The Mathematical Association 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Hagge, K., Der Fuhrmannsche Kreis und der Brocardsche Kreis, Zeitschrift für Math. Unterricht, 38 (1907).Google Scholar
2. Peiser, A. M., The Hagge circle of a triangle, (Amer. Math. Monthly) 49, (1942) pp. 524–527.CrossRefGoogle Scholar
3. Johnson, R. A., Modern geometry, Houghton Mifflin Co. (1929).Google Scholar
4. Bradley, C. J., Challenges in geometry, Oxford University Press (2005).Google Scholar
5. Coxeter, H. S. M. & Greitzer, S. L., Geometry revisited, Math. Assoc. America (1967).Google Scholar
6. Lalesco, T., La géométrie du triangle, (2nd edn.), Jacques Gabay, Paris (reprinted 1987).Google Scholar
7. Manin, Yu. I., Cubic forms, North Holland, Amsterdam (1974).Google Scholar
8. Kimberling, C., Encyclopedia of Triangle Centers – ETC, http://faculty.evansville.edu/ck6/encyclopedia/ETC.html Google Scholar