Circle theorems

Checking and securing understanding of the parts of a circle

The angle at the centre of the circle is twice the angle at any point on the circumference

The angle in a semicircle is a right angle

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

The tangent at any point on a circle is perpendicular to the radius at that point

The angles in the same segment are equal

The alternate segment theorem

The opposite angles of a cyclic quadrilateral sum to 180°

The tangents from an external point are equal in length

Identifying which circle theorem to use

Problem solving with circle theorems