angle at center is double the angle at circumference

We can see a circle in black color. Its center is A and points B, C, D and E are present on its circumference. Angles CAB and CDE are drawn. Angle CDE=α and you can change its value using its slide bar. Move the points A, B, C and D and see how the size and position of the circle gets changed
Questions to think about 1. Using the slide bar let us set the value of α such that angle CAB = 2α, what do we observe? 2. Move only point D, what do we observe