8,9 $[\quad$ Inscribed angle, based on the diameter

In triangle $A B C$, it is known that $\angle B A C=\alpha, A C=b$. The inscribed circle touches the sides $A B$ and $B C$ at points $M$ and $N$, the bisector of angle $B A C$ intersects the line $M N$ at point $K$. Find the distance from point $K$ to the line $A C$.