Thread: circle geomtry II

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.

Originally Posted by the undertaker

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?