Circle Theorems (The Sheet Definitions)

Question 1

Angle at the centre

Answer 1

The angle at the centre is twice the angle at the circumference (standing on the same chord)

Question 2

Angles in the same segment

Answer 2

Angles at the circumference standing on the same chord in the same segment are equal

Question 3

Angles in a semicircle

Answer 3

Angles at the circumference standing on a diameter are equal to 90°

Question 4

Cyclic quadrilaterals

Answer 4

A quadrilateral whose 4 vertices lie the circumference of a circle is called a cyclic quadrilateral.
Opposite angles of a cyclic quadrilateral add up to 180° (supplementary angles)

Question 5

Tangents to a circle

Answer 5

A tangent to a circle is always perpendicular to a radius at the point of contact (90° angle).
Two tangents drawn from the same point are equal in length.

Question 6

Alternate segment

Answer 6

The angle between the tangent and a chord is equal to any angle made by that chord in the alternate segment.