CN-LEAGUE 2007 Problem 1

In an acute triangle $ABC$ , $AB<AC$ . $AD$ is the altitude dropped onto $BC$ and $P$ is a point on $AD$ . Let $PE\perp AC$ at $E$ , $PF\perp AB$ at $F$ and let $J,K$ be the circumcentres of triangles $BDF, CDE$ respectively. Prove that $J,K,E,F$ are concyclic if and only if $P$ is the orthocentre of triangle $ABC$ .