Myths about teaching can hold you back
- Year 10•
- Higher
Problem solving with circle theorems
I can use my knowledge of circle theorems to solve problems.
- Year 10•
- Higher
Problem solving with circle theorems
I can use my knowledge of circle theorems to solve problems.
Lesson details
Key learning points
- Circle theorems can be used in situations involving circles
- It is not always obvious that a circle theorem can be used
- Sometimes you may wish to add more to a diagram in order to deduce more information
Keywords
Tangent - A tangent of a circle is a line that intersects the circle exactly once.
Chord - A chord is any line segment joining two points on the circumference of a circle.
Perpendicular - Two lines are perpendicular if they meet at right angles.
Equidistant - Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.
Common misconception
Pupils may not recognise or confuse which circle theorems to apply in a multi-step problem.
Encourage pupils to add more to a diagram in order to deduce more information about the problem. Drawing an additional line segment, such chord or radius may a useful first step.
To help you plan your year 10 maths lesson on: Problem solving with circle theorems, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Problem solving with circle theorems, 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
Prior knowledge starter quiz
6 Questions
Q1.$$a$$° = °.

Q2.Calculate the size of angle $$b$$°.

Q3.The diagram shows a circle with a tangent and three line segments that form a triangle inside the triangle.
$$c$$° = °.

Q4.$$d$$° = °.

Q5.Points A and B are points where two separate tangents intersect the circle.
$$c$$° = °.

Q6.Points A and B are points where two separate tangents intersect the circle.
Find the size of angle $$d$$°.

Assessment exit quiz
6 Questions
Q1.The length of chord MN is cm (2 d.p.).

Q2.$$a$$° = ° (2 d.p.).

Q3.$$u = 7k + 4$$.
$$v = 9k$$.
$$u$$° = °.

Q4.$$m + k = 207$$.
$$k$$° = °.

Q5.The image shows a circle, a tangent to the circle and a number of chords and radii within the circle.
$$b : c : d = 5 : 7 : 6$$.
$$e$$° = °.

Q6.The image shows a circle, a tangent to the circle and a number of chords and radii within the circle.
$$b : c : d = 5 : 7 : 6$$.
$$g : h = 14 : 9$$.
$$h$$° = °.
