Question 125
Points $K$ and $L$ are chosen on a side $AB$ of a convex quadrilateral $ABCD$, with $K$ lying between $A$ and $L$. Similarly, points $M$ and $N$ are chosen on a side $CD$, with $M$ lying between $C$ and $N$. It appears that $AK = KN = DN$ and $BL = BC = CM$. Given that $BCNK$ is a cyclic quadrilateral, prove that $ADML$ is also cyclic. (T. Zimanov, P. Kozhevnikov)