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A theorem on concurrent Euler lines

Published online by Cambridge University Press:  01 August 2016

C. J. Bradley
C. J. Bradley*
Affiliation:
6A Northcote Road, Clifton, Bristol BS8 3HB
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Extract

In the configuration, illustrated in Figure 1, ABC is a triangle with I1; I2, I3 the excentres opposite A, B, C respectively. The triangles I1BC, I2CA, I3AB are denoted by T1, T2, T3 respectively. Ok, Hk, are the circumcentre, orthocentre respectively of triangle Tk, k = 1, 2, 3. Lk is the Euler line of Tk, k = 1, 2, 3. Define the point Ek (t) on Lk by the equation

Type
Articles
Information
The Mathematical Gazette , Volume 90 , Issue 519 , November 2006 , pp. 412 - 416
Copyright
Copyright © The Mathematical Association 2006

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References

1. Bradley, C.J., Challenges in Geometry for Mathematical Olympians, Oxford University Press (2005).Google Scholar
2. Gardiner, A.D. and Bradley, C.J., Plane Euclidean Geometry: Theory and Problems, The United Kingdom Mathematics Trust (2005).Google Scholar
3. Sommerville, D.M.Y., Analytical Conies, George Bell and Sons (1961) p. 187.Google Scholar