Question 58
Let $B,C$ be fixed, non-diametrically opposite points on a circle with centre $O$. Let $A$ vary on the circle, distinct from $B,C$ and not on the perpendicular bisector of $BC$. Let $H$ be the orthocentre of $ABC$, and $M,N$ the midpoints of $BC,AH$, respectively. Line $AM$ meets the circle again at $D$, and $NM$ meets $OD$ at $P$. Determine the locus of $P$ as $A$ moves around the circle.