Year 10 Specialist Mathematics Circle Theorem Proofs

Comprehensive study notes for Year 10 Specialist Mathematics covering all major circle theorems. This document provides clear, step-by-step proofs for each theorem, complete with diagrams.

These notes are an excellent resource for exam preparation and cover the following topics:

Chord Properties 📝

• Proofs that equal chords subtend equal angles at the centre and are equidistant from the centre.
• Proof that a perpendicular line from the centre of a circle bisects a chord.

Angles in a Circle 📐

• Proof that the angle at the centre is double the angle at the circumference.
• Proof for angles in the same segment and that the angle in a semicircle is a right angle (90∘).
• Proofs for cyclic quadrilaterals, including that opposite angles are supplementary.

Tangents, Secants, and Intersecting Chords 🌐

• The Alternate Segment Theorem proof.
• Proofs for the Intersecting Chords, Intersecting Secant, and Intersecting Secant & Tangent theorems.