Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-11T06:58:50.910Z Has data issue: false hasContentIssue false
  • English
  • Français

Steiner-Lehmus and the Feuerbach triangles

Published online by Cambridge University Press:  01 August 2016

C. F. Parry
C. F. Parry*
Affiliation:
73 Scott Drive, Exmouth EX8 3LF
Get access Rights & Permissions [Opens in a new window]

Extract

In the geometry of the triangle, the Feuerbach quadrangle comprises the four points of contact between the nine point circle and the four tritangent circles. By omitting each of the four points in turn, we create four Feuerbach triangles. When the basic triangle is isosceles we find that two of the four points of contact coincide and the resultant single Feuerbach triangle is also isosceles. In the spirit of Steiner-Lehmus we address the converse question – if one of the Feuerbach triangles is isosceles, is the basic triangle necessarily isosceles? The answer is negative.

Type
Articles
Information
The Mathematical Gazette , Volume 79 , Issue 485 , July 1995 , pp. 275 - 285
Copyright
Copyright © The Mathematical Association 1995

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. Court, N.A., College Geometry, Barnes & Noble, New York (1952).Google Scholar
2. A bibliographical note, Math. Gaz. 18 (May 1934) p. 120.CrossRefGoogle Scholar
3. Durell, C.V. & Robson, A., Advanced Trigonometry, G. Bell (1950).Google Scholar
4. Problem Corner, Math. Gaz. 76 (November 1992) p. 458.Google Scholar
5. Parry, C.F., A variation on the Steiner-Lehmus theme, Math. Gaz. 62 (June 1978) p. 89.CrossRefGoogle Scholar