MathNet 2015-part-04 — 191 problems (EN–VI) Question 165

Let $M$ be the midpoint of the side $[AC]$ of triangle $ABC$ and $N \in (AM)$. The parallel from $N$ to $AB$ intersects $BM$ in $P$, the parallel from $M$ to $BC$ intersects $BN$ in $Q$ and the parallel from $N$ to $AQ$ intersects $BC$ in $S$. Prove that the straight lines $PS$ and $AC$ are parallel.

Cosmin Manea, Dragoş Petrică