Circle Theorems

Question 1

What are the circle theorems?

Answer 1

There are 7 main circle theorems:

1. Alternate segment theorem
2. Angle at the centre is twice the angel at the circumference
3. Angles in the same segment are equal
4. Angle is semi circle
5. Chord of a circle
6. Tangent of a circle
7. Cyclic Quadrilateral

Question 2

What circle theorem is this?

Answer 2

Alternate Segment Theorem

The angle that lies between a tangent and a chord is equal to the angle subtended by the same chord in the alternate segment

Question 3

What circle theorem is this?

Answer 3

Angle at centre theorem

The angle at the centre is twice the angle at the circumference

Question 4

What circle theorem is this?

Answer 4

Angles in same segment theorem

Angles in the same segment are equal

Question 5

What circle theorem is this?

Answer 5

Angles in a semicircle

The angle is a semicircle is 90 degrees

Question 6

What circle theorem is this?

Answer 6

Chord of circle

The perpendicular from the centre of a circle to a chord bisects the chord (splits chord in two equal parts)

Question 7

What circle theorem is this?

Answer 7

Cyclic Quadrilateral

The opposite angles in a cyclic quadrilateral total 180 degrees

Question 8

What circle theorem is this?

Answer 8

Tangent of a circle part A

The angle between a tangent and a radius is 90 degrees

Question 9

What circle theorem is this?

Answer 9

Tangent of a circle part B

Tangents which meet at the same point are equal in length