Question 93
In an acute triangle $ABC$ such that $|AC| \lt |BC|$, points $M$ and $N$ are respectively the feet of altitudes from vertices $A$ and $B$. The circumcircle of the triangle $ABC$ with the centre $O$ and the circumcircle of the triangle $MNC$ with the centre $S$ intersect in points $C$ and $D$. If the point $P$ is the midpoint of the segment $\overline{AB}$, prove that points $P$, $O$, $S$ and $D$ lie on the same circle. (Stipe Vidak)