The Alternate Segment Theorem (Cambridge (CIE) IGCSE International Maths): Revision Note

Alternate segment theorem

Circle theorem: The alternate segment theorem

• The angle between a chord and a tangent is equal to the angle in the alternate segment

  • The alternate segment is the region on the opposite side of a chord from a given angle formed between that chord and a tangent line

• To spot this circle theorem on a diagram

  • look for a cyclic triangle

    • where all three vertices of the triangle lie on the circumference

  • one vertex of the triangle meets a tangent

• To identify which angles are equal

  • mark the angle between the tangent and the side of the cyclic triangle

  • the angle inside the triangle at the corner opposite the side of the triangle that forms the first angle is the equal angle

• When explaining this theorem in an exam you can just say the phrase:

  • The Alternate segment theorem