Question 37
In a convex cyclic hexagon $A B C D E F$, $B C = E F$ and $C D = A F$. Diagonals $A C$ and $B F$ intersect at point $Q$, and diagonals $E C$ and $D F$ intersect at point $P$. Points $R$ and $S$ are marked on the segments $D F$ and $B F$ respectively so that $F R = P D$ and $B Q = F S$. The segments $R Q$ and $P S$ intersect at point $T$. Prove that the line $T C$ bisects the diagonal $D B$.