Let $H$ be the orthocenter of an acute-angled triangle $ABC$ and $P$ a point on the circumcenter of triangle $ABC$. Prove that the Simson line of $P$ bisects the segment $[P H]$.
Problem
Source: 2013 Romania JBMO TST2 P4
Tags: bisects segment, geometry, Simson line, orthocenter, circumcircle