CZ-SK-MO 2007 Problem 5

In an acute-angled triangle $ABC$ ( $AC\ne BC$ ), let $D$ and $E$ be points on $BC$ and $AC$ , respectively, such that the points $A,B,D,E$ are concyclic and $AD$ intersects $BE$ at $P$ . Knowing that $CP\bot AB$ , prove that $P$ is the orthocenter of triangle $ABC$ .