Circle Theorem: Angle at the Centre — Interactive Lesson (Ages 14–16)

Why is the angle at the centre double the angle at the circumference? This 19-slide interactive lesson teaches the angle at the centre theorem, with a proof students can follow.

Mastering the Angle at the Centre Theorem at GCSE

Students learn to state the theorem: the angle at the centre of a circle is twice the angle at the circumference from the same two points on the same chord. Key vocabulary such as subtended, arc, circumference and chord is explained, and a proof outline uses isosceles triangles formed by radii. A worked example finds multiple angles, and students then apply the theorem to unknown angles.

What’s Included

• 19-slide interactive lesson on the angle at the centre theorem
• Learning objectives: state, understand, apply and prove the theorem
• Key vocabulary including subtended, arc and chord
• A proof outline using isosceles triangles
• Quiz, fill-in-the-blank and sorting activities with instant feedback

Key Benefits for Students

• Explains why the theorem works, not just what it says
• Builds the exam vocabulary of circle theorems
• Practises finding unknown angles
• Instant feedback on answer questions

Why Teachers Love It

• No prep — ready for whole-class teaching on an interactive whiteboard
• Includes a proof for stronger students
• Self-marking questions support independent practice
• Suits teaching, revision and homework
• Fits neatly into a circle theorems unit

Love this? You’ll love…

• Circle Theorems Angles In A Semi Circle — Interactive Lesson (KS4)
• Circle Theorem: Cyclic Quadrilaterals — Interactive Lesson (Ages 14–16)
• Circle Theorem: Angles in the Same Segment — Interactive Lesson (Ages 14–16)

A dependable addition to a GCSE circle theorems unit, giving students both the rule and the reasoning behind it. Secure understanding here supports cyclic quadrilaterals and angles in the same segment.

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FAQ

What year group is this for? Years 10–11 (ages 14–16), GCSE.

Does it include a proof? Yes — a proof outline using isosceles triangles.

Is it self-marking? Yes, with instant feedback on the questions.