This exam tips covers Common Mistakes 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 5 of 6 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.
Common Mistakes
X Angle at circumference = 2× angle at centre
Angle at CENTRE = 2× angle at circumference
Don't reverse the relationship!
X Adjacent angles in cyclic quad = 180°
OPPOSITE angles in cyclic quad = 180°
Must be opposite, not adjacent
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!