circle theorums

Question 1

Alternate segment theorem

Answer 1

The angle that lies between a tangent and a chord is equal to the angle subtended by the same chord in the alternate segment

Question 2

Angle at the centre theorem

Answer 2

The angle at the centre is twice the angle at the circumference

Question 3

Angles in the same segment theorem

Answer 3

Angles in the same segment are equal

Question 4

Angles in a semicircle theorem

Answer 4

The angle in a semicircle is 90 degrees

Question 5

Chord of a circle theorem

Answer 5

The perpendicular from the centre of a circle to a chord bisects the the chord (splits the chord into two equal parts)

Question 6

Cyclic Quadrilateral Theorum

Answer 6

The opposite angles in a cyclic quadrilateral total 180

Question 7

Tangent of a Circle Theorum

Answer 7

A) The angle between a tangent and a radius is 90 degrees
B) Tangents which meet at the same point are equal in length