Circle Theorems

Question 1

How do you subtend an angle from two points?

Answer 1

You draw lines from the two points to a single point on the circumference of the circle. The angle between those two lines is subtended.

Question 2

What is the relationship between an angle subtended by an arc at the centre and an angle subtended on the circumference?

Answer 2

The angle at the centre is double the one on the circumference. You can prove this by splitting the angle so that there are two triangles. You can then solve it algebraically.

Question 3

What is the relationship between two angles subtended by the same two points?

Answer 3

They are equal, as all are double the angle subtended at the centre.

Question 4

What is a cyclic quadrilateral, and in it, what do opposite angles add up to?

Answer 4

A cyclic quadrilateral is a quadrilateral with corners that all touch the circumference of an imaginary circle. Opposite angles in such a shape will always add up to 180°.

Question 5

What is the angle subtended by the diameter?

Answer 5

90°

Question 6

What is the angle between a tangent and a radius?

Answer 6

90°

Question 7

What is the relationship between two tangents that meet at the same point?

Answer 7

They are equal in length. This is true because if you split the quadrilateral formed into two right angled triangles, the hypotenuse and radius is the same.

Question 8

What does a perpendicular from the centre two a chord do to the chord?

Answer 8

It bisects it.

Question 9

What is the alternate segment theorem?

Answer 9

It states that the between a tangent and a chord is equal to the angle subtended by that chord.