GCSE Maths (Edexcel)

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Alternate Segment Theorem

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Geometry and Measures Properties and Constructions

Alternate Segment Theorem

5:54 Even More Circle Theorems
Spec G10
Previous Opposite Angles in a Quadrilateral Next Circle Theorem Problems
  • The alternate segment of a circle is the segment formed by the same chord but the arc on the other side.
  • The angle formed between a tangent and a chord is equal to the angle from that chord in the alternate segment of the circle.
  • The alternate segment theorem can be proven using other circle theorems and properties of triangles.
  • Steps to prove the alternate segment theorem:
  • 1. Draw a diameter from the point where the tangent touches the circle.
  • 2. Join the other end of the diameter to the other end of the chord.
  • 3. Use a theorem to deduce the angle where the new line meets the first chord.
  • 4. Use a theorem to deduce the angle between the first chord and the diameter.
  • 5. Use the sum of the angles in a triangle to deduce the size of the missing angle in the triangle.
  • 6. Use a theorem to deduce the size of the given angle from the chord.
  • The angles at the circumference subtended by the same arc are equal.

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