Proofs using cyclic quadrilaterals

9.G.C.3

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Angles in the same segment of a circle are equal. if a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle. The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180 degree and its converse.