Question 79
Let $O$ be the circumcentre of the acute triangle $ABC$. Let $H$ denote the orthocentre and let $D$ be the foot of the altitude from $C$. The line perpendicular to $OD$ at $D$ intersects the segment $BC$ at $E$. The circumcircle of the triangle $BCH$ intersects the line $AB$ at $B$ and $F$. Prove that the points $E, F$ and $H$ lie on the same line.