# 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.

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