Question 177
Let $ABCDEF$ be a convex hexagon. The diagonals $AC$ and $BD$ cross at $P$, the diagonals $AE$ and $DF$ cross at $Q$, and the line $PQ$ crosses the sides $BC$ and $EF$ at $X$ and $Y$, respectively. Prove that the length of the segment $XY$ does not exceed the sum of the lengths of one of the diagonals through $P$ and one of the diagonals through $Q$.