Let be the circumcenter and the orthocenter of an acute-angled triangle such that . Let be the foot of the altitude of triangle . The perpendicular to the line at the point intersects the line at . Prove that .
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Let $O$ be the circumcenter and $H$ the orthocenter of an acute-angled triangle $ABC$ such that $BC>CA$. Let $F$ be the foot of the altitude $CH$ of triangle $ABC$. The perpendicular to the line $OF$ at the point $F$ intersects the line $AC$ at $P$. Prove that $\measuredangle FHP=\measuredangle BAC$.
Source: Međunarodna matematička olimpijada, shortlist 1996
Školjka 
be the circumcenter and 
the orthocenter of an acute-angled triangle 
such that 
. Let 
be the foot of the altitude 
of triangle 
at the point 
at 
. Prove that 
.