Y by
Let A, B, C, and D be four distinct points on a straight line, in that order. The circles with diameters AC and BD intersect at X and Y. The straight line XY intersects BC at Z. Let P be a point on XY distinct from Z. The straight line CP intersects the circle with diameter AC at C and M, and the straight line BP intersects the circle with diameter BD at B and N. Show that AM, DN, and XY are aligned.