Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T07:08:07.540Z Has data issue: false hasContentIssue false
  • English
  • Français

Notes on the Brocard points and angles of a triangle

Published online by Cambridge University Press:  02 March 2020

Sadi Abu-Saymeh  and
Mow Affaq Hajja
Sadi Abu-Saymeh
Affiliation:
2271 Barrowcliffe Drive, Concord, NC 28027, USA P. O. Box 963708, 11196 – Amman – Jordan
Mow Affaq Hajja
Affiliation:
P. O. Box 388 – Al-Husun, 21510 – Irbid – Jordan, Jordan e-mails: ssaymeh@yahoo.com; mowhajja@yahoo.com
Get access Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Articles
Information
The Mathematical Gazette , Volume 104 , Issue 559 , March 2020 , pp. 49 - 62
Copyright
© Mathematical Association 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Leversha, G., The geometry of the triangle, The United Kingdom Mathematics Trust, Pathways, No. 2, University of Leeds (2013).Google Scholar
Yff, P., On the Brocard points of a triangle, Amer. Math. Monthly 67 (1960) pp. 520–525.CrossRefGoogle Scholar
Shail, R., Some properties of Brocard points, Math. Gaz. 80 (November 1996) pp. 485–491.CrossRefGoogle Scholar
Johnson, R. A., Advanced Euclidean Geometry, Dover Publications, New York (1929).Google Scholar
Abu-Saymeh, S. and Hajja, M., Some Brocard-like points of a triangle, Forum Geom. 5 (2005) pp. 65–74.Google Scholar
Yff, P., An analogue of the Brocard points, Amer. Math. Monthly, 70 (1963) pp. 495–501.CrossRefGoogle Scholar
Goormaghtigh, M. R., Sur deux points du plan d’un triangle et sur une généralisation des points de Brocard, Ann. de. Mathémat., 4° série, t. XVIII, (Novembre 1918) pp. 417–424.Google Scholar
Niven, I., Maxima and minima without calculus, The Dolciani Mathematical Expositions, No. 6, MAA, Washington, D. C. (1981).Google Scholar
Isaacs, I. M., Geometry for college students, AMS, Providence, RI (2001).Google Scholar
Kuczma, M. E., International Mathematical Olympiads, 1986-1999, MAA, Washington, D. C. (2003).CrossRefGoogle Scholar
Rigby, J., A method for obtaining related inequalities, with applications, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 412-460 (1973), pp. 217–226.Google Scholar
Bradley, C. J., Challenges in geometry, Oxford University Press, New York (2005).Google Scholar
Clement, P. E., The concurrence of perpendiculars, Amer. Math. Monthly, 65 (1958) pp. 601–605.CrossRefGoogle Scholar
Andreescu, T., Korsky, S. and Pohoata, C., Lemmas in Olympiad geometry, XYZ Press, LLC (2016).Google Scholar
Choi, M. D., Lam, T. Y. and Reznick, B., Even symmetric sextics, Math. Z. 195 (1987) pp. 559–580.CrossRefGoogle Scholar
Hajja, M., Copositive symmetric cubic forms, Amer. Math. Monthly, 112 (2005) pp. 462–466.CrossRefGoogle Scholar
Hajja, M., Radical and rational means of degree 2, Math. Inequal. Appl. 6 (2003) pp. 581–593.Google Scholar
Habeb, J. and Hajja, M., A method for establishing certain trigonometric inequalities, J. Inequal. Pure Appl. Math. (JIPAM) 8 (2007) Art. 29.Google Scholar