circle theorems

alternate segment theorem

• angle that lies between a tangent

• and a chord

• is equal to the angle subtended by the same chord

• in the alternate segment

tangent of a circle theorem

• angle between a tangent

• and a radius

• is always 90°

• tangents which meet at the same point

• are equal in length

chord of a circle theorem

• angle between

• the midpoint of a chord

• and the radius

• is always 90°

angles at the centre theorem

• angles at the circumference

• are half

• angles at the centre

angles in a semi-circle theorem

• angles in semi-circles

• are always 90°

cyclic quadrilateral theorem

• opposite angles

• in a cyclical quadrilateral

• always add up to 180°

angles in the same segment theorem

• angles in the same segment

• are equal