Circle Theorems

AQA Specification Reference G10

Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results 1. Angle subtended by an arc at the centre is equal to twice the angle subtended at any point on the circumference 2. Angle subtended at the circumference by a semicircle is 90° 3. Angles in the same segment are equal 4. Opposite angles in a cyclic quadrilateral sum to 180°, 5. Tangent at any point on a circle is perpendicular to the radius at that point 6. Tangents from an external point are equal in length, 7. The perpendicular from the centre to a chord bisects the chord, 8. Alternate segment theorem.