Cyclic quadrilateral and alternate segment

[grzz]

As the secant AE is moved downwards, the exterior angle remains equal to the same interior angle, with the result that as the secant becomes a tangent, the cyclic quadrilateral disappears and the exterior angle becomes equal to the angle in the alternate segment. pdf is attached.It is interesting to see a property of the cyclic quadrilateral being transformed into a property of the alternate segment.Any other geometrical examples like the above?

 

[grzz]

The post included all I had to say.
Thanks.