Geometry: Circle Theorems

Circle theorems describe key angle and length relationships in circles. At GCSE you are expected to know, apply and cite all eight theorems, and in some cases prove them.

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Circle Vocabulary (Review)

Term	Definition
Centre	The fixed middle point
Radius (r)	Distance from centre to any point on the circle
Diameter (d)	Chord through the centre; d = 2r
Chord	A straight line joining two points on the circle
Arc	Part of the circumference
Sector	Region bounded by two radii and an arc
Tangent	A line touching the circle at exactly one point
Segment	Region between a chord and an arc
Cyclic quadrilateral	A quadrilateral with all four vertices on the circle

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The Eight Circle Theorems

Theorem 1: Angle at the Centre

The angle subtended at the centre of a circle is twice the angle subtended at the circumference by the same arc.

Angle AOB = 2 × angle ACB (where O is the centre)

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