Circle Theorems

Question 1

What does circle theorem 1 state?

Answer 1

Angles in the same segment are equal. It is often referred to as the ‘bow tie’ shape.

Question 2

What does circle theorem state?

Answer 2

The angle at the centre of the circle is twice the angle on the circumference.

Question 3

What does circle theorem 3 state?

Answer 3

The angle in a semicircle equals 90 degrees.

In other words, if there is a diameter and a line to the circumference and back to the other side of the diameter the angle is 90 degrees.

Question 4

What does circle theorem 4 state?

Answer 4

Opposite angles within a cyclic quadrliateral add up to 180 degrees. All four vertices of the quadrilateral much touch the circumference.

Question 5

What does circle theorem 5 state?

Answer 5

The line from the centre to the circumference bisects a chord that is goes through (each angle on the line equals 90 degrees as a result).

Question 6

What does circle theorem 6 state?

Answer 6

The angle between a tangent and a chord is equal to the angle in the alternate segment.

Question 7

What does circle theorem 7 state?

Answer 7

The angle between a radius and a tangent is equal to 90 degrees.

Question 8

What does circle theorem 8 state?

Answer 8

Two tangents which meet at a point outside a circle are equal in length.