VN-TST 2009 Problem 5

Let a circle $(O)$ with diameter $AB$ . A point $M$ move inside $(O)$ . Internal bisector of $\widehat{AMB}$ cut $(O)$ at $N$ , external bisector of $\widehat{AMB}$ cut $NA,NB$ at $P,Q$ . $AM,BM$ cut circle with diameter $NQ,NP$ at $R,S$ . Prove that: median from $N$ of triangle $NRS$ pass over a fix point.