First circle theorem: 'Angle at centre'

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Angle at centre and angle at circumference

First circle theorem:

What's the connection between the angle at the centre, α, and the angle at the circumference, β?

You can use the cursor to move point B, and hence to alter angle α.
You can also move point D around the circumference.
If you move point C, then angle α and the size of the circle both change.
Notice what happens to angle β as you make these changes.

If you need it, this theorem is set out here

and all the theorems are summarised here

Tim Devereux, Created with GeoGebra