KöMaL 2021 B5173

The orthocentre of an acute-angled triangle $ABC$ is $H$, and the centre of the circumscribed circle is $O$. Let $D$ and $E$ denote interior points on the line segments $AB$ and $AC$, respectively. The orthocentre and circumcentre of triangle $ADE$ are $H'$ and $O'$, respectively. Show that lines $HH'$ and $OO'$ are parallel if and only if $BD = CE$.