Circle theorems

Question 1

Answer 1

Angles subtended in the same arc are equal.

Question 2

Answer 2

The angle subtended in the semicircle is 90°. (Or the angle subtended by the diameter is 90°).

Question 3

Answer 3

The angle between a tangent and a radius is 90°

Question 4

Answer 4

Two tangents to the circle from a single point have equal length

Question 5

Answer 5

Alternate segment.

Question 6

Answer 6

Alternate angles are equal - only on parallel lines.

Question 7

Answer 7

Corresponding angles are equal - but only on parallel lines.

Question 8

Answer 8

Opposite angles of a cyclic quadlilateral add up to 180°

Question 9

Answer 9

The perpendicular from the centre of the circle to the chord bisects the chord.

Question 10

What is the formula for calculating the sum of the interior angles of a polygon?

Answer 10

(n-2) x 180

Question 11

What do the exterior angles of a polygon always add up to?

Answer 11

360°

Question 13

Angles subtended in the same arc are equal.

Answer 13

Question 14

The angle subtended in the semicircle is 90°. (Or the angle subtended by the diameter is 90°).

Answer 14

Question 15

The angle between a tangent and a radius is 90°

Answer 15

Question 16

Two tangents to the circle from a single point have equal length

Answer 16

Question 17

Alternate segment.

Answer 17

Question 18

Alternate angles are equal - only on parallel lines.

Answer 18

Question 19

Corresponding angles are equal - but only on parallel lines.

Answer 19

Question 20

Opposite angles of a cyclic quadlilateral add up to 180°

Answer 20

Question 21

The perpendicular from the centre of the circle to the chord bisects the chord.

Answer 21