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On Napoleon triangles and propeller theorems

Published online by Cambridge University Press:  01 August 2016

Zvonko Čerin
Zvonko Čerin*
Affiliation:
Kopernikova 7, 10010 Zagreb, Croatia. email: cerin@math.hr
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Extract

In this paper we shall consider two situations in triangle geometry when equilateral triangles appear and then show that they are closely related.

In the first (known as the Napoleon theorem) equilateral triangles BCAT, CABT, and ABCT, are built on the sides of an arbitrary triangle ABC and their centroids are (almost always) vertices of an equilateral triangle ANBNCN (known as a Napoleon triangle of ABC; see Figure 1).

Type
Articles
Information
The Mathematical Gazette , Volume 87 , Issue 508 , March 2003 , pp. 42 - 50
Copyright
Copyright © The Mathematical Association 2003

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