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Geometry & MeasuresDeep Dive

Solving Circle Theorem Problems

Part of Circle Theorems — GCSE Mathematics

This deep dive covers Solving Circle Theorem Problems within Circle Theorems for GCSE Mathematics. Revise Circle Theorems in Geometry & Measures for GCSE Mathematics with 18 exam-style questions and 5 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 3 of 5 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 5

Practice

18 questions

Recall

5 flashcards

Solving Circle Theorem Problems

1Mark all known angles on the diagram
2Identify key features: centre, diameter, tangent, chord, cyclic quadrilateral
3Look for isosceles triangles - any two radii form one!
4Apply the relevant theorem(s) - often need multiple
5State the theorem you used (required for full marks!)

Keep building this topic

Read this section alongside the surrounding pages in Circle Theorems. That gives you the full topic sequence instead of a single isolated revision point.

The Eight Circle TheoremsWorked Example: Centre and CircumferenceThe Geometry of PizzaCommon Mistakes

Practice Questions for Circle Theorems

AB is a diameter of a circle. Point C lies on the circle. What is the size of angle ACB?

  • A. 45°
  • B. 60°
  • C. 90°
  • D. 180°
1 markfoundation

State the circle theorem used to find angle x in the diagram, and explain why it applies in this situation.

2 marksstandard

Quick Recall Flashcards

Angle in Semicircle
Any angle inscribed in a semicircle (with diameter as base) is always 90°. Always!
Cyclic Quadrilateral
If all 4 vertices lie on a circle, opposite angles sum to 180°. Also works in reverse: if opposite angles sum to 180°, then it's cyclic!

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The Eight Circle Theorems

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Worked Example: Centre and Circumference