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Long medians and long angle bisectors

Published online by Cambridge University Press:  13 October 2021

Sadi Abu-Saymeh,
Yaqeen Al-Momani,
Mowaffaq Hajja and
Mostafa Hayajneh
Sadi Abu-Saymeh
Affiliation:
2271 Barrowcliffe Dr., Concord, NC 28027, USA, e-mail: ssaymeh@yahoo.com
Yaqeen Al-Momani
Affiliation:
Mathematics – Ajloun National University Ajloun – Jordan, e-mail: yaqeenal-momany@yahoo.com
Mowaffaq Hajja
Affiliation:
Mathematics – Philadelphia University Amman – Jordan, e-mail: mowhajja@yahoo.com
Mostafa Hayajneh
Affiliation:
Mathematics – Yarmouk University Jordan, e-mail: hayaj86@yahoo.com

Extract

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Following Euler, we denote the side lengths and angles of a triangle ABC by a, b, c, A, B, C in the standard order. Any line segment joining a vertex of ABC to any point on the opposite side line will be called a cevian, and a cevian AA′ of length t will be called long, strictly long, or balanced according as t ≥ a, t > a or t = a. If A′ lies strictly between B and C, AA′ is called an internal cevian. This convention regarding cevians is not universal, and it is, for example, in a heavy contrast with that in [1, p. 73].

Information

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 564 , November 2021, pp. 397 - 409
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Copyright
© The Mathematical Association 2021

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