Circle Theorems

Question 0

Arrowhead

Answer 0

The angle subtended at the centre of the circle is double the size of the angle at the circumference from the same points.

Question 1

Butterfly

Answer 1

Angles in the same segment of a circle are equal

Question 2

Wheel on a flat surface

Answer 2

The angle between the tangent and radius is 90 degrees

Question 3

Diameter triangle

Answer 3

The inscribed angle in a semicircle is 90 degrees

Question 4

Rectangle

Answer 4

Opposite angles in a cyclic quadrilateral add up to 180 degrees

Question 5

Triangle in circle on flat surface

Answer 5

Alternate segment theorem

Question 6

Arrow from circumference of circle

Answer 6

Tangents from a point outside the circle are equal in length

Question 7

From centre triangle

Answer 7

The perpendicular from the centre to the chord bisects the chord