
06144259
j
2013f.00514
AbuSaymeh, Sadi
Hajja, Mowaffaq
Equicevian points on the altitudes of a triangle.
Elem. Math. 67, No. 4, 187195 (2012).
2012
European Mathematical Society (EMS) Publishing House, Zurich
EN
G45
triangle
cevian
equicevian point
doi:10.4171/EM/209
Let $ABC$ be a triangle. Consider a point $P\neq B$ a point in the plane containing $ABC$ such that $BP$ is not parallel to $AC$. We denote (it it exists) by $BB_P$ the cevian from $B$ through $P$. In the same way, if $P\neq C$ and $CP$ is not parallel to $AB$, we could define $CC_P$. In this situation a point $P$ is called $A${\it equicevian} if the lengths of $BB_P$ and $CC_P$ are equal. The paper under review is concerned to $A$equicevian points lying on the altitude $AO$ from $A$. In passing, some remarks concerning the (somewhat ubiquitous) polynomials $p(X,Y,Z)=X^3+Y^3+Z^33XYZ$ and $q(T)=T^3(\alpha^2\beta^2\gamma^2)T+2\alpha\beta\gamma$ are made.
Antonio M. Oller (Zaragoza)