MathNet 2003 — Part 01 Question 182

$C$ is a point on the semicircle with diameter $AB$. $D$ is a point on the arc $BC$. $M$, $P$, $N$ are the midpoints of $AC$, $CD$ and $BD$. The circumcenters of $ACP$ and $BDP$ are $O$, $O'$. Show that $MN$ and $OO'$ are parallel.