Proof

1
Proof

• Applying Mathematics Solving Problems

2
The 24 Point Circle

• All points are equally spaced around the
  circumference.
• Join two consecutive points to the centre.
• How would you work out the angle at the centre?

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4
The 24 Point Circle

• To find one angle at the centre the following
  calculation is used-
• 3600
• 24
• 150

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6
The 24 Point Circle

• Look at the three triangles what is special
  about them?
• How can we work out the angle at the centre of
  each of these triangles?
• Therefore, how can we calculate each of the
  angles of the triangle?

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Angles in a Triangle

• Angle at 3 37?0 37?0 750
• Angle at 10 150 37?0 52?0
• Angle at 20 150 37?0 52?0
• Angle Sum of Triangle 750 52?0 52?0
• 1800

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Angles in a Triangle
10
Circle Theorem
11
Circle Theorem
12
Circle Theorem

• What have you noticed about the angle at the
  centre and its opposite angle on the
  circumference?

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Circle Theorem