KöMaL 2025 B5460

In acute triangle $ABC$ let $D$, $E$ and $F$ denote the feet of the altitudes from $A$, $B$ and $C$, respectively. Let line $DE$ intersect circle $ABC$ at points $G$, $H$. Similarly, let line $DF$ intersect circle $ABC$ at points $I$, $J$. Prove that the radical axis of circles $EIJ$ and $FGH$ passes through the orthocenter of triangle $ABC$.