Question 164
Let $k$ be the incircle of a scalene triangle $\triangle A B C$, with center $S$. The circle $k$ touches the sides $B C, C A, A B$ at the points $P, Q, R$, respectively. The line $Q R$ meets the line $B C$ at the point $M$. Let a circle through the points $B$ and $C$ touch $k$ at the point $N$. The circumcircle of $\triangle M N P$ meets the line $A P$ at a point $L$ different from $P$. Prove that the points $S, L$ and $M$ are collinear.