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