IGCSE normal math circle theorem and simple geometry

Alternate segment therem

The angle that lies between a tangent and a chord in a circle 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 semicircle

The angle in a semicircle is 90 degres.

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 a cyclic quadrilateral total 180 degrees.

Tangent of a circle (1)

The angle between a tangent and the radius is 90 degrees.

Tangent of a circle (2)

Tangents which meet at the same point are equal in length.

Exterior angle

Sum of the interior angles except the opposite angle equals the exterior angle

Corresponding angles

Corresponding angles are equal

Alternating Angles

Alternating angles are euqal

Opposite angles

Vertically opposite angles are equal

Co-interior angles

Co-interior angles add up to 180 degrees