Question 10
A segment $AB$ and its midpoint $K$ are given. An arbitrary point $C$, different from $K$, is chosen on the perpendicular to $AB$ through $K$. Let $N$ be the intersection of $AC$ and the line passing through $B$ and the midpoint of the segment $CK$. Let $U$ be the intersection of $AB$ with the line that passes through $C$ and the midpoint $L$ of the segment $BN$. Prove that the ratio of the areas of the triangles $CNL$ and $BUL$ doesn't depend on the choice of point $C$.