Geometry & MeasuresStudy Notes

Worked Example: Centre and Circumference

Part of Circle TheoremsGCSE Mathematics

This study notes covers Worked Example: Centre and Circumference 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 4 of 5 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 5

Practice

18 questions

Recall

5 flashcards

Worked Example: Centre and Circumference

Points A, B, C lie on a circle with centre O. Angle AOC = 124°. Find angle ABC.

Step 1 Identify the theorem

AOC is at the centre, ABC is at the circumference

→ Use Theorem 1: angle at centre = 2× angle at circumference

Step 2 Apply the theorem

124° = 2 × Angle ABC

Angle ABC = 124° ÷ 2 = 62°

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.

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

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!
Angle in Semicircle
Any angle inscribed in a semicircle (with diameter as base) is always 90°. Always!

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