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perpendicular from center of a circle to chord bisects chord

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. We can change the value of α using its slide bar. Move these 5 points A, B, C, D and E and observe how the size of the circle and length of EC and DE get changed.