Segment joining midpoint of any chord of a circle and center

We can see a circle in black color. A is the center of the circle and B is any point present on the circumference of this circle. CD is any chord of the circle. Point E is any point present on this chord. We have joined the points E and A. Length of the segments CE and ED are also written in black color. Angle CEA is α. Move these 5 points A, B, C, D and E and observe how the size of the circle, length of EC and DE and angle α gets changed
Questions to think about 1. Move the points C, D and E in such a way that EC = DE, what do you observe? (It is possible that we will not be able to make EC = DE by manually moving the points, try to make EC and DE as equal as possible).