Question 90
Let $ABC$ be an acute, non-isosceles triangle with the orthocenter $H$, circumcenter $O$ and $AD$ is the diameter of $(O)$. Suppose that the circle $(AHD)$ meets the lines $AB$, $AC$ at $F$, $E$, respectively. Denote $J$, $K$ as orthocenter and nine-point center of $AEF$. Prove that $HJ$ is parallel to $BC$ and $KO = KH$.