Circle Theorems

Question 1

What is the angle at the centre theorem?

Answer 1

The angle at the centre of a circle is twice the angle at the circumference (both should be from the same chord).

Question 2

What is the angle in a semicircle theorem?

Answer 2

Any angle formed in a semicircle is a right angle (90°).

Question 3

What does “angles in the same segment” mean?

Answer 3

Angles in the same segment, standing on the same chord, are equal.

Question 4

What’s special about opposite angles in a cyclic quadrilateral?

Answer 4

Opposite angles in a cyclic quadrilateral add up to 180°.

Question 5

What is the tangent–radius angle rule?

Answer 5

A tangent meets a radius at 90°.

Question 6

What do we know about the two tangents from the same (external) point?

Answer 6

Tangents from the same point to a circle are equal in length.

(and make equal angles with the line joining the point to the centre)

Question 7

What does the alternate segment theorem say?

Answer 7

The angle between a tangent and a chord equals the angle in the opposite/alternate segment.

Question 8

What’s true about a perpendicular bisector a chord?

Answer 8

The perpendicular bisector of a chord goes through the centre of a circle