KöMaL 2018 B4926

In an acute-angled triangle $ABC$, the feet of the altitudes drawn from $B$ and from $C$ are $D$ and $E$, respectively. The reflections of point $E$ in the lines $AC$ and $BC$ are $S$ and $T$, respectively. The circle $CST$, centred at $O$, intersects line $AC$ again at point $X\ne C$. Show that lines $XO$ and $DE$ are perpendicular.