A. 529. There is given a circle k on the plane, a chord AB of k, furthermore four interior points, C, D, E and F, on the line segment AB. Draw an arbitrary chord X1X2 of k through point C, a chord Y1Y2 through D, a chord U1U2 through E, finally a chord V1V2 through F in such a way that X1, Y1, U1 and V1 lie on the same side of the line AB, and
holds. Let Z be the intersection of the lines X1X2 and Y1Y2, and let W be the intersection of U1U2 and V1V2. Show that the lines ZW obtained in this way are concurrent or they are parallel to each other.
Deadline expired on 10 March 2011.