1.3.6    an angle in a semicircle is a right angle

1.3.9    the opposite angles of a cyclic quadrilateral are supplementary. x+y=180

1.3.12    when two chords of a circle intersect, the product of the lengths of the intervals on one chord equals the product of the lengths of the intervals on the other chord. (AE × CE = DE × BE)

Tangents drawn to a circle from an external point are of equal length.

1.3.7    the size of the angle at the centre subtended by an arc of a circle is twice the size of the angle at the circumference subtended by the same arc

1.3.10    chords of equal length subtend equal angles at the centre, and conversely, chords subtending equal angles at the centre of a circle have the same length

1.3.13    when a secant (meeting the circle at A and B) and a tangent (meeting the circle at T) are drawn to a circle from an external point M, the square of length of the tangent equals the product of the lengths to the circle on the secant (AM × BM = TM²)

1.3.8    angles at the circumference of a circle subtended by the same arc are equal

1.3.11    the angle in the alternate segment theorem

A tangent drawn to the circle is perpendicular to the radius at point of contact.