Math Circle TheoremsCIRCLE The angle subtended by an arc at the centre is twice the angle subtended at the circumference

Angles subtended by an arc in the same segment of a circle are equal.

The angle in a semi-circle is a right angle. [or if a triangle is inscribed in a semi-circle the angle opposite the diameter is a right angle].

Opposite angles of a cyclic quadrilateral add up to (supplementary). The corners touch the circle. The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.( = )

CHORDa) The line from the centre of a circle to the mid-point of a chord bisects the chord at right angles. Lb) The line from the centre of a circle to the mid-point of a chord bisects the angle subtended by the chord at the centre of the circle. TANGENTS The angle between a tangent and the radius drawn to the point of contact is

From any point outside a circle just two tangents to the circle may be drawn and they are of equal length. TA = TB

Alternate Segment Theorem The angle between a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the alternate segment.