The paper deals with the following construction generalizing work by {\it F. van Lamoen} [Forum Geom. 13, 149‒152 (2013; Zbl 1287.51018)]: Given an arbitrary point $A$, on the side $BC$ of a given triangle $ABC$, construct on $BC$ points $P$ and $P’$ isotomic with respect to $B$ and $C$ such that the parallels from $P$, $P’$ to $AA’$ meet $AB$ and $AC$ at points $Q$, $Q’$ such that, in the trapezoid $QPP’Q’$ it holds that $QQ’=PQ’P’Q’$. The authors show how to perform this construction and investigate some interesting properties. Just like in van Lamoen’s work, some background or motivation would have been highly appreciated.

Reviewer:

Antonio M. Oller (Zaragoza)