KöMaL 2025 C1877

Let $D$, $E$ and $F$ be the midpoints of the arcs $BC$, $CA$ and $AB$ not containing points $A$, $B$ and $C$, respectively, on the circumcircle of acute triangle $ABC$. Line segment $DE$ intersects sides $BC$ and $CA$ in points $P$ and $Q$, respectively. Line segment $EF$ intersects sides $CA$ and $AB$ in points $R$ and $S$, respectively. Line segment $FD$ intersects sides $AB$ and $BC$ in points $T$ and $U$, respectively. Prove that triangles $PRT$ and $QSU$ have equal areas.