BG-MO 1989 Problem 1

In triangle $ABC$ , point $O$ is the center of the excircle touching the side $BC$ , while the other two excircles touch the sides $AB$ and $AC$ at points $M$ and $N$ respectively. A line through $O$ perpendicular to $MN$ intersects the line $BC$ at $P$ . Determine the ratio $AB/AC$ , given that the ratio of the area of $\triangle ABC$ to the area of $\triangle MNP$ is $2R/r$ , where $R$ is the circumradius and $r$ the inradius of $\triangle ABC$ .