Second circle theorem: 'Angle in a semicircle'

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Angle in a semicircle

Second circle theorem:

There are 2 Geogebra windows here; newer one just below, & original lower down.

For the first one, try moving the point P about. Where does P have to be for angle α to be acute? and where must P be for angle α to be obtuse? So where must P be to make angle α  =  90 degrees?

What happens to angle α as you move P? (Bit dull, as I expect you've worked out that there is an angle bigger than acute, but smaller than obtuse....)

If you need it, this theorem is set out here

and all the theorems are summarised here

Tim Devereux, Created with GeoGebra