On plane there is fixed ray $s$ with vertex $A$ and a point $P$ not on the line which contains $s$. We choose a random point $K$ which lies on ray. Let $N$ be a point on a ray outside $AK$ such that $NK=1$. Let $M$ be a point such that $NM=1,M \in PK$ and $M!=K.$ Prove that all lines $NM$, provided by some point $K$, touch some fixed circle.