\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2013f.00514}
\itemau{Abu-Saymeh, Sadi; Hajja, Mowaffaq}
\itemti{Equicevian points on the altitudes of a triangle.}
\itemso{Elem. Math. 67, No. 4, 187-195 (2012).}
\itemab
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 $q(T)=T^3-(\alpha^2-\beta^2-\gamma^2)T+2\alpha\beta\gamma$ are made.
\itemrv{Antonio M. Oller (Zaragoza)}
\itemcc{G45}
\itemut{triangle; cevian; equicevian point}
\itemli{doi:10.4171/EM/209}
\end