Let be the circumcenter and the orthocenter of an acute triangle Show that there exist points and on sides and respectively such that and the lines and are concurrent.
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Let $O$ be the circumcenter and $H$ the orthocenter of an acute triangle $ABC.$ Show that there exist points $D, E,$ and $F$ on sides $BC,CA,$ and $AB$ respectively such that $$OD + DH = OE +EH = OF +FH$$ and the lines $AD, BE,$ and $CF$ are concurrent.
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Školjka 
be the circumcenter and 
the orthocenter of an acute triangle 
Show that there exist points 
and 
on sides 
and 
respectively such that 
and the lines 
and 
are concurrent.