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Twenty-one points on the nine-point circle

Published online by Cambridge University Press:  01 August 2016

Clark Kimberling*
Affiliation:
Department of Mathematics, University of Evansville, 1800 Lincoln Avenue, Evansville, Indiana 47722, USA, e-mail: ck6@evansville.edu

Extract

The nine points for which the nine-point circle is named are the vertices of three triangles: the medial, orthic, and Euler triangles of a reference triangle ABC. All nine of the vertices lie on the circle, which Dan Pedoe [1] proclaims ‘the first really exciting one to appear in any course on elementary geometry’. An online summary of properties of the circle, which is also called the Euler circle, is given at MathWorld [2].

Type
Articles
Copyright
Copyright © The Mathematical Association 2008

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References

1. Pedoe, Daniel, Circles, Pergamon, New York (1957).Google Scholar
2. Weisstein, Eric, MathWorld, http://mathworld.wolfram.com/.Google Scholar
3. Kimberling, Clark, Triangle centers and central triangles, Congressus Numerantium, 5. 129, i–xxv, 1–295. Utilitas Mathematica, University of Manitoba, Winnipeg, 1998.Google Scholar
4. Kimberling, Clark, Encyclopedia of triangle centers-ETC, http:// faculty.evansville.edu/ck6/encyclopedia/ETC.html.Google Scholar
6. Prasolov, V.V., planimetrii, Zadachi po, Moscow, , Biblioteka matematicheskogo kruzhka, 15,16, Moscow (1991).Google Scholar