KöMaL 2019 A748

The circles $\Omega$ and $\omega$ in its interior are fixed. The distinct points $A$, $B$, $C$, $D$, $E$ move on $\Omega$ in such a way that the line segments $AB$, $BC$, $CD$ and $DE$ are tangents to $\omega$. The lines $AB$ and $CD$ meet at point $P$, the lines $BC$ and $DE$ meet at $Q$. Let $R$ be the second intersection of the circles $BCP$ and $CDQ$, other than $C$. Show that $R$ moves either on a circle or on a line.