id: 06144259
dt: j
an: 2013f.00514
au: Abu-Saymeh, Sadi; Hajja, Mowaffaq
ti: Equicevian points on the altitudes of a triangle.
so: Elem. Math. 67, No. 4, 187-195 (2012).
py: 2012
pu: European Mathematical Society (EMS) Publishing House, Zurich
la: EN
cc: G45
ut: triangle; cevian; equicevian point
ci:
li: doi:10.4171/EM/209
ab: 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 $p(X,Y,Z)=X^3+Y^3+Z^3-3XYZ$ and
$q(T)=T^3-(α^2-β^2-γ^2)T+2αβγ$ are made.
rv: Antonio M. Oller (Zaragoza)