IGCSE Maths / Circle theorems

The alternate segment theorem

Edexcel International GCSE Maths (4MA1), chapter 17: Circle theorems, specification point 4.6c. Part of the full course.

Read the revision notes · IGCSE Maths past papers

The alternate segment theorem links the angle between a tangent and a chord to an angle on the far side of that chord. It lets you find the matching angle directly, and naming the theorem in full earns a reason mark.

More lessons in Circle theorems

• Parts of a circle and cyclic quadrilaterals
• Tangent and radius, and two tangents from a point
• The angle at the centre is twice the angle at the circumference
• The angle in a semicircle
• Angles in the same segment
• Opposite angles of a cyclic quadrilateral
• Using the alternate segment theorem in a reasoning chain
• Reasoning chains with circle theorems
• Multi-step circle theorem problems
• Intersecting chords inside a circle
• Intersecting chords from a point outside the circle