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Equicevian points on the altitudes of a triangle. (English)
Elem. Math. 67, No. 4, 187-195 (2012).
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.
Reviewer: Antonio M. Oller (Zaragoza)
Classification: G45
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