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We are going to explore the connection between the angle at the centre of a circle and the angle at any point on the circumference.
Label the centre of the circle then add three points to the circumference and label them A, B and C.
Select points A and B, right-click and choose Line Segment. Repeat for BC, OA and OC.
What do you think the angle at the circumference is? What about the angle at the centre? Select points A, B then C, right-click and choose Angle.
Move point B around the circle.
Move point A around the circle. What do you notice?
Can you make a conjecture about the angle at the centre of a circle and the angle at any point on the circumference?
Can you prove this conjecture? Can you demonstrate this proof in Autograph?