Circle theorems

1

The angle at the centre of a circle is twice the angle at the circumference when both subtended by the same arc

2

Every angle subtended at the circumference of a semicircle by the diameter is a right angle

3

Angles subtended at the circumference in the same segment of a circle are equal

4

The sum of the opposite angles of a cyclic quadrilateral is equal to 180*

5

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

6

Tangents to a circle from an external point to the points of contacts are equal

7

The line joining an external point to the centre of the circle bisects the angle between the tangents

8

A radius bisects a chord at 90* and 0 is the centre of the circle

9

Alternate segment theorem