Question 3
(CHN 2) The diagonals of a quadrilateral $ABCD$ are perpendicular: $AC\perp BD$. Four squares, $ABEF$, $BCGH$, $CDIJ$, $DAKL$, are erected externally on its sides. The intersection points of the pairs of straight lines $CL,DF$; $DF,AH$; $AH,BJ$; $BJ,CL$ are denoted by $P_1,Q_1,R_1,S_1$, respectively, and the intersection points of the pairs of straight lines $AI,BK$; $BK,CE$; $CE,DG$; $DG,AI$ are denoted by $P_2,Q_2,R_2,S_2$, respectively. Prove that $P_1Q_1R_1S_1\cong P_2Q_2R_2S_2$.