1. Is the angle in a triangle in a semi-circle always equal to 90o?

Yes, the angle not on the diameter is always 90o

2. Is the angle at the centre of a circle always twice the size of the angle at the circumference?

Yes, providing both angles are in the same segment or same side of the circle.

3. Are angles on the same arc always equal?

Yes, providing they touch the circumference and start and finish on the same arc.