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Generalisation of an IMO geometry problem

Published online by Cambridge University Press:  20 June 2025

Dina Kamber Hamzić ,
László Németh  and
Zenan Šabanac
Dina Kamber Hamzić
Affiliation:
University of Sarajevo, Department of Mathematics and Computer Science, Zmaja od Bosne 33-35, 71000 Sarajevo, Bosnia and Herzegovina e-mail: dinakamber@pmf.unsa.ba
László Németh
Affiliation:
University of Sopron, Institute of Basic Sciences, Bajcsy-Zsilinszky 4, 9400 Sopron, Hungary e-mail: nemeth.laszlo@uni-sopron.hu
Zenan Šabanac
Affiliation:
University of Sarajevo, Department of Mathematics and Computer Science, Zmaja od Bosne 33-35, 71000 Sarajevo, Bosnia and Herzegovina e-mail: zsabanac@pmf.unsa.ba
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Extract

According to Mitchelmore [1], generalisations are the cornerstone of school mathematics, covering various aspects like numerical generalisation in algebra, spatial generalisation in geometry and measurement, as well as logical generalisations in diverse contexts. The process of generalising lies at the heart of mathematical activity, serving as the fundamental method for constructing new knowledge [2, 3]. In this paper we will generalise an interesting geometry problem that appeared in the 1995 edition of the International Mathematical Olympiad (IMO) [4].

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Type
Articles
Information
The Mathematical Gazette , Volume 109 , Issue 575 , July 2025 , pp. 273 - 280
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Copyright
© The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association

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