Last one...
Diagonals of quadrilateral $ABCD$ intersect in point $S$. Circle $k_1$ is circumscribed of triangle $ABS$. $k_1$ intersects line $BC$ in point $M$. Circle $k_2$ is circumscribed of triangle $ADS$ and it intersects line $CD$ in point $N$. Prove that points $S, M$ and $N$ are collinear.