parmenides51 wrote: On the sides $AB$ and $CD$ of the parallelogram $ABCD$ mark points $E$ and $F$, respectively. On the diagonals $AC$ and $BD$ chose the points $M$ and $N$ so that $EM\parallel BD$ and $FN\parallel AC$. Prove that the lines $AF, BE$ and $MN$ intersect at one point. (B. Rublev) The last sentence can be re-written as: Prove that the lines $AF, BE$ and $MN$ are concurrent.

parmenides51 wrote: On the sides $AB$ and $CD$ of the parallelogram $ABCD$ mark points $E$ and $F$, respectively. On the diagonals $AC$ and $BD$ chose the points $M$ and $N$ so that $EM\parallel BD$ and $FN\parallel AC$. Prove that the lines $AF, BE$ and $MN$ intersect at one point. (B. Rublev) I think it need to be "Prove that the lines $AF, DE$ and $MN$ intersect at one point." For solution: Pappus.

there was a typo, the correct was $AF,DE,MN$ and not $AF,BE,MN$