OME 1985 Problem 6

Let $OX$ and $OY$ be non-collinear rays. Through a point $A$ on $OX$ , draw two lines $r_1$ and $r_2$ that are antiparallel with respect to $\angle XOY$ . Let $r_1$ cut $OY$ at $M$ and $r_2$ cut $OY$ at $N$ . (Thus, $\angle OAM = \angle ONA$ ). The bisectors of $\angle AMY$ and $\angle ANY$ meet at $P$ . Determine the location of $P$ .