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Some triangle theorems by complex numbers

Published online by Cambridge University Press:  11 October 2023

John R. Silvester
John R. Silvester*
Affiliation:
Department of Mathematics, King’s College, Strand, London WC2R 2LS e-mail: [email protected]
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The following theorems appear in [1, pp. 62-63]: Theorem 1 If similar triangles A1B0C0, A0B1C0, A0B0C1 are erected externally on the sides of ΔA0B0C0, then the circumcircles of these three triangles have a common point, F.

Type
Articles
Information
The Mathematical Gazette , Volume 107 , Issue 570 , November 2023 , pp. 454 - 473
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Copyright
© The Authors, 2023 Published by Cambridge University Press on behalf of The Mathematical Association

References

Coxeter, H. S. M. and Greitzer, S. L., Geometry revisited, The Mathematical Association of America (1967).CrossRefGoogle Scholar
Leversha, Gerry, The geometry of the triangle, The United Kingdom Mathematics Trust (2013).Google Scholar
Johnson, Roger A., Advanced euclidean geometry, Dover (2007).Google Scholar
Suzuki, Fukuzo, Generalisations of the Napoleon theorems, and triangles circumscribing a given triangle, Math. Gaz. 92 (March 2008), pp. 115–124.CrossRefGoogle Scholar
Čerin, Zvonko, On Napoleon triangles and propellor theorems, Math. Gaz. 87 (March 2003), pp. 42–50.CrossRefGoogle Scholar
Coxeter, H. S. M., Introduction to geometry, Wiley (1961).Google Scholar
Silvester, John R., Extensions of a theorem of Van Aubel, Math. Gaz. 90 (March 2006), pp. 2–12.CrossRefGoogle Scholar