Problem

Source: China Southeast Math Olympiad 2014 No.3

Tags: geometry, incenter, AMC, USA(J)MO, USAMO, geometry unsolved



In an obtuse triangle $ABC$ $(AB>AC)$,$O$ is the circumcentre and $D,E,F$ are the midpoints of $BC,CA,AB$ respectively.Median $AD$ intersects $OF$ and $OE$ at $M$ and $N$ respectively.$BM$ meets $CN$ at point $P$.Prove that $OP\perp AP$