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Twenty-one points on the nine-point circle

Published online by Cambridge University Press:  01 August 2016

Clark Kimberling
Clark Kimberling*
Affiliation:
Department of Mathematics, University of Evansville, 1800 Lincoln Avenue, Evansville, Indiana 47722, USA, e-mail: ck6@evansville.edu
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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
Information
The Mathematical Gazette , Volume 92 , Issue 523 , March 2008 , pp. 29 - 38
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
5. Grinberg, Darij, [EMHL] Prasolov point X(68), http://mathforum.org/ kb/thread.jspa?forumID=125&threadID=349623&messageID= 1071627#1071627 Google Scholar
6. Prasolov, V.V., planimetrii, Zadachi po, Moscow, , Biblioteka matematicheskogo kruzhka, 15,16, Moscow (1991).Google Scholar