Circle theorems
All eight, in the exact wording examiners want for the reason in a proof — that's where the marks are won and lost. Flip on Test yourself to drill them.
Write these word-for-word as your reason — that's where the marks are.
1. Angle at the centre
The angle at the centre is twice the angle at the circumference (subtended by the same arc).
2. Angle in a semicircle
The angle in a semicircle is 90°.
3. Angles in the same segment
Angles in the same segment are equal.
4. Cyclic quadrilateral
Opposite angles of a cyclic quadrilateral add up to 180°.
5. Tangent and radius
A tangent is perpendicular to the radius at the point of contact.
6. Two tangents
Two tangents drawn from an external point are equal in length.
7. Alternate segment
The angle between a tangent and a chord equals the angle in the alternate segment.
8. Perpendicular to a chord
The perpendicular from the centre to a chord bisects the chord.
Learn the language of proofs
“State”, “prove”, “show that” — each wants a different kind of answer.
Command words guideStruggling with maths? The first tutoring lesson is free.
Free revision tool by Oscar Song Tutoring