KöMaL 2007 A438

On the circumcircle of the equilateral triangle ABC , choose an arbitrary point $P$ on arc $AB$. Mark the points $Q$ and $R$ on arc $BC$ and the points $S$ and $T$ on arc $CA$ for which $AP$=$BQ$=$CR$=$CS$=$AT$ holds. Let lines $BQ$ and $PR$ meet at $U$ and let lines $AS$ and $PT$ meet at $V$. Finally, let lines $AU$ and $BV$ meet at $W$. Show that each two of lines $AU$, $BV$and $PW$ enclose an angle of $60^o$.