Question 2
Let $\omega$ be a circle with centre $O$ and distinct points $A,C$ on it. For any point $P$ on $\omega$ distinct from $A,C$, let $X,Y$ be the midpoints of $AP,CP$. Let $H$ be the orthocentre of triangle $OXY$. Prove that the position of $H$ does not depend on the choice of $P$.