The circles w1 and w2 intersect at points P and Q. Let AB and CD be parallel diameters of circles w1 and w2, respectively. In this case, none of the points A,B,C,D coincides with either P or Q, and the points lie on the circles in the following order: A,B,P,Q on the circle w1 and C,D,P,Q on the circle w2. The lines AP and BQ intersect at the point X, and the lines CP and DQ intersect at the point Y,X=Y. Prove that all lines XY for different diameters AB and CD pass through the same point or are all parallel.(Serdyuk Nazar) geometryparallelconcurrentcircles