IMO Shortlist 1991 problem 3


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Let S be any point on the circumscribed circle of 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.
Izvor: Međunarodna matematička olimpijada, shortlist 1991