Circle Theorems

Question 1

State the rule for:

An angle at the point of an arrow head is half the angle enclosed at the centre

Answer 1

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

Question 2

cyclic quadrilateral

Answer 2

The sum of the opposite angles of a cyclic quadrilateral is 180

Question 3

Radius and chord

Answer 3

A radius bisects a chord at 90°

Question 4

Right angle triangle in a semi circle

Answer 4

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

Question 5

Tangent and radius

Answer 5

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

Question 6

Tangent length

Answer 6

Tangents to a circle from an external point to the points of contact are equal in length

Question 7

Tangent angles

Answer 7

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

Question 8

Angles on the circumference are the same if the lines come from the same point

Answer 8

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

Question 9

The angle between a tangent and a chord through the point of contact is equal to the alternate segment

Answer 9

Alternate segment theorem