Angles at the Centre and Circumference

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In the circle below, arc AB subtends angle APB at the circumference and angle AOB at the centre of the circle.

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Drag point A or B to different locations and observe the relation between angle APB and angle AOB?

Hint: Calculate the ratio of angle AOB to angle APB

 

Extension:
Drag A and B such that angle AOB = 180o

 

What happens to angle APB?  Move point P around the circle and observe the angle.