Circle Theorems And Constructions

A circle looks simple, but the angles hiding inside it obey a tight web of rules: an angle at the centre is always exactly twice its counterpart on the circumference, opposite corners of a cyclic quadrilateral are always supplementary, and a tangent meets its radius at a perfect right angle every time. This topic gives you the full set of Edexcel circle theorems, proved rather than just stated, plus the loci and constructions that turn these ideas into precise ruler-and-compasses drawings.

You will learn to identify which theorem a diagram is asking for, chase an angle through several steps of reasoning, and construct an angle bisector and a perpendicular bisector using nothing but a straight edge and compasses. Circle theorem questions reward students who can name the exact property they used, so this note treats every reason as seriously as the number attached to it.