2 circles meet @ points A & B. Points X & Y of these circles are diametrically opposite to point A.
Prove that X, Y and B are collinear.
Diametrically opposite means opposite along the diameter. As usual, make a sketch.
You will need to use the fact that the angle in a semicircle is 90 degree.
so angle XBA=angle YBA=90 and that is the sum of angles along a straight line.
What can you deduce from here?