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The Mathematical Gazette
Article . 1955 . Peer-reviewed
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Triangles With Common Circumcentre and Orthocentre

Triangles with common circumcentre and orthocentre
descriptionPublicationkeyboard_double_arrow_right Article 01 May 1955 English Publisher:Cambridge University Press (CUP)Journal:The Mathematical Gazette, volume 39, pages 106-108 (issn: 0025-5572, eissn: 2056-6328, Copyright policy )
Authors: D.G. Taylor;

doi: 10.2307/3609971

Triangles With Common Circumcentre and Orthocentre

Abstract

1. The object of this paper may be best explained by reference to the figure. ABC is a triangle with circumcentre O and orthocentre P. What other triangles share these points with ABC?There is clearly a doubly infinite family of such triangles. If we confine attention for the moment to those possessing the same circumradius R, we shall have a singly infinite family, which we may call the family R. These also possess in common, in addition to circumcentre and orthocentre,(i) nine-points centre U (the middle point of OP) and nine-points circle, radius ½R ;(ii) centroid G, where (OGUP) is harmonic.

Keywords

elementary geometry

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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