The altitudes through the vertices
of an acute-angled triangle
meet the opposite sides at
respectively. The line through
parallel to
meets the lines
and
at
and
respectively. The line
meets
at
Prove that the circumcircle of the triangle
passes through the midpoint of
%V0
The altitudes through the vertices $A,B,C$ of an acute-angled triangle $ABC$ meet the opposite sides at $D,E, F,$ respectively. The line through $D$ parallel to $EF$ meets the lines $AC$ and $AB$ at $Q$ and $R,$ respectively. The line $EF$ meets $BC$ at $P.$ Prove that the circumcircle of the triangle $PQR$ passes through the midpoint of $BC.$
Školjka