Sixth circle theorem: 'Angle between tangent and radius'

Angle between tangent and radius

Sixth circle theorem:

What do you notice about the angle between tangent and radius, α & β?

You can use the cursor to move point C, and you can change the size of the circle by moving point O or X.

If you need it, this theorem is set out here

and all the theorems are summarised here

Tim Devereux, Created with GeoGebra