Question 3
(PRK 1) Let $S$ be any point on the circumscribed circle of $\triangle PQR$. 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 $l(S,PQR)$. Suppose that the hexagon $ABCDEF$ is inscribed in a circle. Show that the four lines $l(A,BDF)$, $l(B,ACE)$, $l(D,ABF)$, and $l(E,ABC)$ intersect at one point if and only if $CDEF$ is a rectangle.