If a hexagon ABCDEF circumscribes a circle, show that AB + CD + EF = BC + DE + FA.

$$\begin{aligned}& PB = BQ \dots (1) \\ & RC = QC \dots (2) \\ & RD = DS \dots (3) \\ & ET = SE \dots (4) \\ & TF = FU \dots (5) \\ & AP = AU \dots (6) \\ & Adding (1), (2), (3), (4), (5)\end{aligned}$$ and $(6)$, we get
$$\begin{aligned}& (AP+ PB)+(RC + RD)+(ET + TF) = (BQ + QC)+(DS + SE)+(FU + AU) \\ & \Rightarrow AB + CD + EF = BC + DE + FA\end{aligned}$$