A limiting circle theorem

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In this interactivity, you can move the points \(A\), \(B\), \(C\) and \(D\) around the circumference of the circle, with \(D\) between \(B\) and \(C\).

1. Three angles are marked.

   What can you say about the angles at \(C\) and \(D\)?

   What happens to these angles if you move \(C\) or \(D\), keeping \(A\) and \(B\) fixed?

   How do you know this?

2. What happens to the exterior angle at \(B\) (shown in blue) as \(D\) approaches \(B\)?

3. Which other circle theorem can you deduce from this?