KöMaL 2019 B5065

The centre of the circumscribed circle of an acute angled triangle $ABC$ is $O$, and the reflections of $O$ in sides $BC$, $CA$ and $AB$ are $O_A$, $O_B$, and $O_C$, respectively. Show that the lines $AO_A$, $BO_B$ and $CO_C$ are concurrent.