1991 IMO 第 3 题

(PRK 1) Let $S$ be any point on the circumscribed circle of $\triangle P Q R$. Then the feet of the perpendiculars from $S$ to the three sides of the triangle lie on the same straight line. Denote this line by $l(S, P Q R)$. Suppose that the hexagon $A B C D E F$ is inscribed in a circle. Show that the four lines $l(A, B D F), l(B, A C E), l(D, A B F)$, and $l(E, A B C)$ intersect at one point if and only if $C D E F$ is a rectangle.

(PRK 1) 设$S$为$\三角形P Q R$的外接圆上的任意点。那么从 $S$ 到三角形三边的垂线的脚位于同一条直线上。用 $l(S, P Q R)$ 表示这条线。假设六边形 $A B C D E F$ 内接于圆。证明四条直线 $l(A, B D F)、l(B, A C E)、l(D, A B F)$ 和 $l(E, A B C)$ 相交于一点当且仅当 $C D E F$ 是矩形时。