Circle Theorems

Question 1

Angle at the centre is ? the angle at the ?

Answer 1

Angle at the centre is double the angle at the circumference.

Question 2

Angle in a semicircle is ? ‘

Answer 2

Angle in a semicircle is 90 ‘

Question 3

Opposite angles in a ? add up to ?

Answer 3

Opposite angles in a cyclic quadrilateral add up to 180 ‘

Question 4

Angles in the same segment are ?

Answer 4

Angles in the same segment are equal.

Question 5

The radius meets a ? at ? ‘

Answer 5

The radius meets a tangent at 90 ‘

Question 6

Tangents which meet at the same point are ? in length

Answer 6

Tangents which meet at the same point are equal in length

Question 7

Which circle theorem is this?

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

Answer 7

Alternate segment theorem