Let be the circumcenter of an acute triangle . Line intersects the altitudes of through and at and , respectively. The altitudes meet at . Prove that the circumcenter of triangle lies on a median of triangle .
Let $O$ be the circumcenter of an acute triangle $ABC$. Line $OA$ intersects the altitudes of $ABC$ through $B$ and $C$ at $P$ and $Q$, respectively. The altitudes meet at $H$. Prove that the circumcenter of triangle $PQH$ lies on a median of triangle $ABC$.
Školjka 
be the circumcenter of an acute triangle 
. Line 
intersects the altitudes of 
and 
at 
and 
, respectively. The altitudes meet at 
. Prove that the circumcenter of triangle 
lies on a median of triangle