Circle Theorem: Tangents to a Circle — Interactive Lesson (Ages 14–16)

Which circle theorem do I use? This 16-slide interactive lesson teaches the two key facts about tangents to a circle, then applies them to exam-style questions.

Mastering Tangents to a Circle at GCSE

Students learn two geometric facts: the angle between a radius and a tangent is 90°, and the lengths of the tangents from an external point to a circle are equal. Worked examples show how to find angles with reasons, for example when PT is a tangent and angle PTU is 54°, and when PA and PB are tangents with angle APB = 68°. Students choose which theorems apply and compare student answers with reasons.

What’s Included

• 16-slide interactive lesson on tangents to a circle
• The tangent and radius theorem, and the equal tangents theorem
• Worked examples with reasons for each angle
• A question comparing three students’ answers and reasons
• Exam-style questions combining several circle theorems

Key Benefits for Students

• Builds the habit of giving a reason for each step
• Combines tangent facts with isosceles and triangle angle rules
• Prepares students for multi-step exam questions
• Instant feedback on answer questions

Why Teachers Love It

• No prep — ready for whole-class teaching on an interactive whiteboard
• Exam-style questions build test readiness
• 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 Theorems Angle At The Centre — Interactive Lesson (KS4)
• Circle Theorem: Cyclic Quadrilaterals — Interactive Lesson (Ages 14–16)

A dependable addition to a GCSE circle theorems unit, giving students the tangent facts and plenty of practice using them with reasons. Choosing the right theorem is a skill that examiners reward.

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FAQ

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

Does it include exam-style questions? Yes — including a multi-step exam question.

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