3. Circle Theorems The angle at the centre is twice the angle at the circumference for angles which stand on the same arc.

4. Circle Theorems

11. 1) The two tangents from a point to a circle are equal in length. 2) Angles subtended at the circumference by equal arcs are equal. 3) If a pair of opposite angles of a quadrilateral add up to 180 o then it is a cyclic quadrilateral. 4) The angle in a semicircle is a right angle. 5) The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle. 6) The straight line from the centre of a circle at right angles to a chord bisects the chord.

12. Circle Theorems 7) A tangent is perpendicular to the radius at the point of contact. 8) The circle drawn on the hypotenuse of a right-angled triangle as diameter passes through the opposite vertex. 9) Angles in the same segment are equal. 10) The straight line from the centre of a circle to the mid-point of a chord is perpendicular to the chord. 11) The opposite angles of a cyclic quadrilateral add up to 180 o. 12) The angle at the centre is twice the angle at any point on the circumference subtended by the same arc. 13) Equal chords are equidistant from the centre of a circle.