Circle theorems

Learning objectives

Use circle vocabulary: centre, radius, diameter, circumference, chord, tangent, arc, sector and segment

Use the facts that the angle in a semicircle is 90° and that a tangent is perpendicular to the radius at the point of contact

Use the symmetry properties of circles: equal chords are equidistant from the centre, the perpendicular bisector of a chord passes through the centre, and tangents from an external point are equal (Extended)

Use the theorems that the angle at the centre is twice the angle at the circumference and that angles in the same segment are equal (Extended)

Use the facts that opposite angles of a cyclic quadrilateral sum to 180° and the alternate segment theorem (Extended)

Give geometrical reasons in angle calculations that combine circle theorems with other angle facts