Problem A. 529. (February 2011)
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 X_{1}X_{2} of k through point C, a chord Y_{1}Y_{2} through D, a chord U_{1}U_{2} through E, finally a chord V_{1}V_{2} through F in such a way that X_{1}, Y_{1}, U_{1} and V_{1} lie on the same side of the line AB, and
holds. Let Z be the intersection of the lines X_{1}X_{2} and Y_{1}Y_{2}, and let W be the intersection of U_{1}U_{2} and V_{1}V_{2}. Show that the lines ZW obtained in this way are concurrent or they are parallel to each other.
(5 pont)
Deadline expired on 10 March 2011.
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