Question 185
Let $H$ denote the orthocentre of $\triangle ABC$, with circumcircle $\Gamma$. The altitudes $AH$, $BH$, $CH$ intersect $\Gamma$ for the second time at the points $A'$, $B'$ and $C'$, respectively. The circle of diameter $AH$ intersects $\Gamma$ at the points $A$ and $D$. Lines $DC$ and $A'B'$ intersect at $E$, while lines $DB$ and $A'C'$ intersect at $F$. Prove that $EF$ is parallel to $BC$.