Special inscribed trapezoids in a triangle (Q2871651)

The paper deals with the following construction generalizing work by \textit{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 \(QQ'=PQ'P'Q'\).NEWLINENEWLINEThe authors show how to perform this construction and investigate some interesting properties.NEWLINENEWLINEJust like in van Lamoen's work, some background or motivation would have been highly appreciated.