1992 IMO 第 3 题

(CHN 2) The diagonals of a quadrilateral $A B C D$ are perpendicular: $A C \perp B D$. Four squares, $A B E F, B C G H, C D I J, D A K L$, are erected externally on its sides. The intersection points of the pairs of straight lines $C L, D F ; D F, A H ; A H, B J ; B J, C L$ are denoted by $P_{1}, Q_{1}, R_{1}, S_{1}$, respectively, and the intersection points of the pairs of straight lines $A I, B K$; $B K, C E ; C E, D G ; D G, A I$ are denoted by $P_{2}, Q_{2}, R_{2}, S_{2}$, respectively. Prove that $P_{1} Q_{1} R_{1} S_{1} \cong P_{2} Q_{2} R_{2} S_{2}$.

(CHN 2) 四边形 $A B C D$ 的对角线互相垂直：$A C \perp B D$。四个方格 $A B E F、B C G H、C D I J、D A K L$ 竖立在其两侧的外部。直线对 $C L 、 D F 的交点； D F、A H ； AH，BJ； B J、C L$分别用$P_{1}、Q_{1}、R_{1}、S_{1}$表示，直线对$A I、B K$的交点； $B K, C E ; C E、D G ； D G、A I$ 分别用$P_{2}、Q_{2}、R_{2}、S_{2}$ 表示。证明 $P_{1} Q_{1} R_{1} S_{1} \cong P_{2} Q_{2} R_{2} S_{2}$。