Circle theorems – Year 11 maths lesson
Lesson 7 of 17 in the Year 11 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 11 (ages 15–16) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 11 (ages 15–16)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why is the angle in a semicircle always 90°?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Using a theorem without checking the angles come from the same arc. Trace the arc each angle stands on.
- Not giving reasons. Name the theorem for every step.
Tip for home: Draw circles with a compass and test the theorems with a protractor.
What your child will learn
We are learning to use the circle theorems to find missing angles, giving reasons.
Success looks like
- I can use the circle theorems.
- I can find missing angles.
- I can give the reason for each step.
Key words
- chord
- a line joining two points on a circle
- tangent
- a line that touches a circle at one point
- cyclic quadrilateral
- four corners all on a circle
- segment
- the region between a chord and the circle
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Draw several triangles in a semicircle and measure the angle at the edge each time.
The big ideas (for the adult)
The angle at the centre is twice the angle at the circumference from the same arc. The angle in a semicircle is 90°.
Angles in the same segment are equal. Opposite angles of a cyclic quadrilateral add up to 180°.
A tangent meets a radius at 90°; two tangents from a point are equal in length; the alternate segment theorem links a tangent and a chord.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 11 maths lessons
- Volume and surface area
- Trigonometry: SOH CAH TOA
- Sine rule, cosine rule and area of a triangle
- Transformations
- Similarity and congruence
- Vectors
- Factorising
- Inequalities
- Sequences and the nth term
- Quadratic equations
- Iteration
- Functions
- Algebraic fractions
- Graphs of functions
- Algebraic proof and identities
- Growth and decay
Curriculum
National Curriculum for England, Year 11: “{apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results}”
GCSE subject content G10: “apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.