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HomeCIE IGCSE MathematicsGeometry: Circle theorems and angle properties of circles
CIE · IGCSE · Mathematics

Geometry: Circle theorems and angle properties of circles
Practice Questions

40 CIE IGCSE Mathematics questions on Geometry: Circle theorems and angle properties of circles, each with instant feedback and a full examiner-style mark scheme.

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✨ Revision guide includes key terms, worked examples and exam technique for Geometry: Circle theorems and angle properties of circles.

Try 2 sample questions on Geometry: Circle theorems and angle properties of circles

Question 1 · 1 mark · Difficulty 1/3

In the diagram, O is the centre of the circle. Points A, B and C lie on the circumference. Angle AOB = 124°. What is the size of angle ACB?

  1. 56°
  2. 62°
  3. 124°
  4. 236°
Show answer & explanation
✓ Answer: B62°
Award 1 mark for correct application of the angle at centre theorem: the angle at the centre is twice the angle at the circumference standing on the same arc. Angle ACB = 124° ÷ 2 = 62°. A is incorrect — this would be 180° − 124° which is not relevant here. C is incorrect — this confuses the angle at the centre with the angle at the circumference. D is incorrect — this is the reflex angle at the centre, not the angle at the circumference.
Question 2 · 1 mark · Difficulty 1/3

In a circle with centre O, the diameter PQ passes through O. Point R lies on the circumference of the circle such that R is not on PQ. What is the size of angle PRQ?

  1. 45°
  2. 90°
  3. 180°
  4. It depends on the position of R
Show answer & explanation
✓ Answer: B90°
Award 1 mark for recognising the angle in a semicircle theorem: the angle subtended by a diameter at any point on the circumference is always 90°. A is incorrect — this is a common misconception, confusing with isosceles triangle properties. C is incorrect — 180° would be the angle on a straight line, not at the circumference. D is incorrect — the angle is always 90° regardless of where R is positioned on the circumference.
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CIE IGCSE Mathematics: Geometry: Circle theorems and angle properties of circles FAQ

How many CIE IGCSE Mathematics questions on Geometry: Circle theorems and angle properties of circles are there on Kramizo?
Kramizo currently has 40 exam-board-aligned practice questions on Geometry: Circle theorems and angle properties of circles for CIE IGCSE Mathematics, with new questions added every week. Each question gives you instant feedback and a full examiner-style mark scheme that tells you exactly what would earn marks on a real CIE paper. The questions span the full difficulty range — from straightforward recall (level 1) right up to multi-step reasoning and evaluation (level 3) — so the bank works for first-pass revision and final exam-week stress testing alike.
Is Kramizo free for CIE IGCSE students preparing for Mathematics?
Yes — completely free. Every student gets 45 questions a day on the free plan, with no card required and no trial countdown. That free quota works across every subject and every topic in our bank, so you can mix Geometry: Circle theorems and angle properties of circles practice with other Mathematics topics or even switch to a totally different CIE subject without paying anything. Kramizo's optional Pro plan removes the daily cap and adds detailed progress analytics, but the free tier is the real product — used by thousands of GCSE, IGCSE and CSEC students.
Are the Geometry: Circle theorems and angle properties of circles questions aligned to the official CIE IGCSE Mathematics syllabus?
Every question is written against the published CIE IGCSE Mathematics specification, including the exact command words (state, describe, explain, calculate, evaluate, etc.), mark allocations, and difficulty tier you'd see on a real CIE paper. Explanations are written in the style of official examiner mark schemes — they tell you what is being awarded marks and why distractors are wrong, not just whether you got it right. The bank is continually refined to match the latest syllabus updates from CIE.
How is Geometry: Circle theorems and angle properties of circles typically tested on CIE IGCSE Mathematics papers?
Geometry: Circle theorems and angle properties of circles appears across multiple question types on real CIE IGCSE Mathematics papers — most commonly as multiple-choice questions in the objective section, structured short-answer questions in the main paper, and occasionally as part of an extended response. Kramizo's practice bank reflects that mix: 4-option MCQs, true/false statements, fill-in-the-blank key terms, multi-select questions, and ordering questions. Working through the bank gives you exposure to every question style examiners actually use.

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