Myths about teaching can hold you back
- Year 10•
- Higher
The angle at the centre of the circle is twice the angle at any point on the circumference
I can derive and use the theorem: the angle at the centre of the circle is twice the angle at any point on the circumference.
- Year 10•
- Higher
The angle at the centre of the circle is twice the angle at any point on the circumference
I can derive and use the theorem: the angle at the centre of the circle is twice the angle at any point on the circumference.
Lesson details
Key learning points
- A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
- Theorems can be thought of as puzzles to solve, you are showing how to find a result
- In order to use this theorem, you may need to draw a diagram or add more information to an existing one
Keywords
Subtended - An angle can be subtended by a line segment or curve. The legs of the subtended angle meet the endpoints of the line segment or curve.
Arc - An arc of a circle is part of the circle’s circumference.
Radius - The radius is any line segment that joins the centre of a circle to any point on its circumference.
Chord - A chord is any line segment joining two points on the circumference of a circle.
Common misconception
When faced with a quadrilateral which has three vertices on a circle and one vertex at the centre, pupils may think that the interior angle at the centre is twice the angle at the circumference.
The two angles need to be subtended by the same arc for this circle theorem to apply. Therefore, it is the reflex angle at the centre of the circle which is twice the angle at the circumference.
To help you plan your year 10 maths lesson on: The angle at the centre of the circle is twice the angle at any point on the circumference, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: The angle at the centre of the circle is twice the angle at any point on the circumference, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Circle theorems unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.What is the dashed line segment on this circle called?

Q2.The line segment on this circle passes through its centre.
What is the shaded region on this circle called?

Q3.Which of these statements are correct?
Q4.The size of the angle subtended by the chord AB is °.

Q5.Match each circle to their area (3 s.f.)
area = 78.5 cm² -
radius = 5 cm
area = 314 cm² -
diameter = 20 cm
area = 1260 cm² -
circumference = 40π cm
area = 201 cm² -
“circle with diameter 8 more than its radius”
area = 452 cm² -
“circle with radius 12 less than its diameter”
Q6.A 36° angle at the centre (O) of a circle has been subtended by the arc XY.
The circle has a radius of 50 cm.
The area of the shape bound the arc XY and the legs of the 36° angle is cm² (2 s.f.).
Assessment exit quiz
6 Questions
Q1.The size of angle $$x$$° on this 12-point geoboard is °.

Q2.The size of angle $$y$$° on this 12-point geoboard is °.

Q3.Angle $$a$$° is subtended by chord TU on this 12-point geoboard.
$$a$$° = °

Q4.Angle $$b$$° is subtended by chord TU at the circumference of this 12-point geoboard.
$$b$$° = °

Q5.The size of angle $$c$$° is °.

Q6.The size of the angle marked $$d$$° is °.
