Circle theorems

alternate segment theorem

the angle that lies between a tangent and a chord is equal to the angle subtended by the same chord in the alternate segment

angle at the centre theorem

the angle at the centre is twice the angle at the circumference

angles in the same segment theorem

angles in the same segment are equal

angles in a semi circle

the angle in a semi circle is 90 degrees

chord of a circle

the perpendicular from the centre of a circle to a chord bisects the chord (splits the chord into two equal parts

cyclic quadrilateral

the opposite angles in cyclic quadrilateral total to 180 degrees

tangent of a circle A

the angle between a tangent and a radius is 90 degrees

tangent of a circle B

tangents which meet at the same point are equal in length