IMO Shortlist 1995 problem G1

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2. travnja 2012.
Let A,B,C,D be four distinct points on a line, in that order. The circles with diameters AC and BD intersect at X and Y. The line XY meets BC at Z. Let P be a point on the line XY other than Z. The line CP intersects the circle with diameter AC at C and M, and the line BP intersects the circle with diameter BD at B and N. Prove that the lines AM,DN,XY are concurrent.
Izvor: Međunarodna matematička olimpijada, shortlist 1995