Circles and their theorems
Pages
Parts of a circle
Centre, radius, diameter, chord, circumference, tangent, arc.
The angle in a semicircle
An angle subtended by a diameter is 90°.
The angle at the centre
The angle at the centre is double the angle at the circumference on the same.
Angles in the same segment
Angles at the circumference standing on the same arc are equal.
Cyclic quadrilaterals
Opposite angles of a cyclic quadrilateral sum to 180°.
Tangents to a circle
A tangent meets its radius at 90°.
Chords and the centre
The perpendicular from the centre bisects a chord.
The alternate segment theorem
The angle between a tangent and a chord equals the angle in the alternate.
Proving the circle theorems
Proving the standard theorems from radii making isosceles triangles.
Practice
The angle in a semicircle
An angle subtended by a diameter is 90°.
PracticeThe angle at the centre
The angle at the centre is double the angle at the circumference on the same.
PracticeAngles in the same segment
Angles at the circumference standing on the same arc are equal.
PracticeCyclic quadrilaterals
Opposite angles of a cyclic quadrilateral sum to 180°.
PracticeTangents to a circle
A tangent meets its radius at 90°.
PracticeChords and the centre
The perpendicular from the centre bisects a chord.
PracticeCircle theorems review
Applying each theorem and justifying the reason.