2003 OIM Problems/Problem 2

Problem

Let $C$ and $D$ be two points on the semicircle of diameter $AB$ such that $B$ and $C$ are in different semiplanes with respect to the line $AD$. Let $M$, $N$ and $P$ denote the midpoints of $AC$, $DB$ and $CD$, respectively. Let $O_A$ and $O_B$ be the circumcenters of the triangles $ACP$ and $BDP$. Show that the lines $O_AO_B$ and $MN$ are parallel.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also