VN-TST 2015 Problem 2

sorry if this has been posted before .

given a fixed circle $(O)$ and two fixed point $B,C$ on it.point A varies on circle $(O)$ . let $I$ be the midpoint of $BC$ and $H$ be the orthocenter of $\triangle ABC$ . ray $IH$ meet $(O)$ at $K$ , $AH$ meet $BC$ at $D$ , $KD$ meet $(O)$ at $M$ .a line pass $M$ and perpendicular to $BC$ meet $AI$ at $N$ . a) prove that $N$ varies on a fixed circle. b) a circle pass $N$ and tangent to $AK$ at $A$ cut $AB,AC$ at $P,Q$ . let $J$ be the midpoint of $PQ$ .prove that $AJ$ pass through a fixed point.