Imagine a pizza. The crust is the circle's circumference. Cut a slice from the centre? That's two radii making an angle at the centre. But what if you connect two points on the crust to another point ON the crust? That angle is always exactly HALF the centre angle. Circle theorems are about these beautiful relationships!
This introduction covers The Geometry of Pizza 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 1 of 6 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.
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?
State the circle theorem used to find angle x in the diagram, and explain why it applies in this situation.
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!