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sum of opposite angles of cyclic quadrilateral

Author:
Mathguru
We can clearly see the blue graph, it is that of a circle which passes through the point B and has its center at point A. Points C, D, E and F are four points present on the circumference of the circle. A cyclic quadrilateral is drawn by joining these four point C, D, E, and F. Angles CDE, DEF, EFC and FCD are denoted by α, β , y, δ respectively. We can freely move these six points A, B, C, D, E and F. Move these points and observe how the size and positions of the circle and cyclic quadrilateral get changed.