Circle Theorems

Question 1

What is the relationship, when subtended in a circle, of angles at the centre and those at the circumference?

Answer 1

The relationship is:

Angles at the centre are twice those that are subtended at the remaining part of the circumference.

Question 2

What is the relationship between angles supported by the same arc in a circle?

Answer 2

The relationship:

Angles supported by the same arc are equal.

Question 3

What is the relationship between angles supported by the same segment?

Answer 3

The relationship:

Angles supported by the same segment are equal.

Question 4

What theorem relates a tangent and a radius in a circle?

Answer 4

The theorem relating a tangent and a radius in a circle is:

A tengent and a radius meet at right angles.

Question 5

What is the theorem dictating the nature of angles in a semi-circle?

Answer 5

The theorem dictating the nature of angles in a semi-circle is:

Angles in a semi-circle are right angles.

Question 6

State the theorem relating angles in alternates segments.

Answer 6

The theorem relating angles in alternate segments is:

Angles in alternate segments are equal.

A segment is a part of a circle with a triangle removed.