ACT02B Angle at centre and circumference

there is a centre O and an angle at circumference at point C sustained by arc AB. You can move: 1. Point D in the segment as point C to control the size and position of the angle. 2. Points A and B to control the size and position of the angle at point D. Exploration By moving point D, explore under what situation will the angle at circumference has a special relationship with the angle at D. Draw the two different figures obtained during the exploration. Question 1. Is the converse of angle at centre, twice angle at circumference still valid? 2. In what way the arc length of angles sustained by the same arc affects the relationship?