Topics · Edexcel GCSE Maths (1MA1)

Circle theorems: the angle at the centre

Higher only

Circle theorem marks need the angle and the reason, written as a full theorem. Try the angle first.

Exam-style questionNon-calculator2 marks

A, B and C are points on a circle with centre O.

C is on the major arc AB.

Angle AOB = 124°

Work out the size of angle ACB.

Give a reason for your answer.

See why

Move C around the circle. What happens to angle ACB?

Predict first:

New contextNon-calculator3 marks

ABCD is a cyclic quadrilateral.

Angle ABC = $3x$ and angle ADC = $x + 40^\circ$

Work out the value of $x$ .

Circle theorems and angle chains

Short hands-on steps, then exam questions on this topic.

Specification G10 (Higher content): apply and prove the standard circle theorems.
Higher tier only. When a question asks for a reason, write the theorem in full; the mark scheme for that question decides the marks.
Pearson's examiners report reasons written as vague phrases or abbreviations. Write the theorem in full.