Angles at the centre and circumference
- The angle at the centre is twice the angle at the circumference when both stand on the same arc.
- The angle in a semicircle is 90°.
- Angles in the same segment (standing on the same arc) are equal.
Cyclic quadrilaterals
- A cyclic quadrilateral has all four corners on a circle. Its opposite angles add up to 180°.
Tangents and chords
- A tangent meets a radius at 90°.
- Two tangents drawn to a circle from the same outside point are equal in length.
- The perpendicular from the centre to a chord bisects the chord.
Alternate segment theorem
- The angle between a tangent and a chord is equal to the angle in the alternate segment.
- In the exam, give the theorem you used as the reason for each step. Also look for isosceles triangles made by two radii.
Key terms
- Circumference
- The edge of a circle.
- Cyclic quadrilateral
- A quadrilateral with all four corners on a circle.
- Tangent
- A straight line that touches a circle at one point.
- Chord
- A straight line joining two points on a circle.
- Segment
- The region of a circle between a chord and an arc.
- Subtended
- Formed by an arc or chord at a point, such as the angle an arc makes at the centre.
- Alternate segment theorem
- The angle between a tangent and a chord equals the angle in the alternate segment.