Myths about teaching can hold you back
- Year 10•
- Higher
Identifying which circle theorem to use
I can analyse a circle problem and identify and use an appropriate circle theorem to solve it.
- Year 10•
- Higher
Identifying which circle theorem to use
I can analyse a circle problem and identify and use an appropriate circle theorem to solve it.
Lesson details
Key learning points
- There are many circle theorems so it is important to be clear about each one
- Extra lines can be added to a diagram to help determine which theorem to use
- Some problems require the use of more than one theorem
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 conflate cyclic quadrilaterals with cases of "the angle at the centre of a circle is twice the angle at the circumference" theorem, when the angle at the centre is a reflex angle.
While the two diagrams may look similar at a glance, pay extra attention to whether all four points of the quadrilateral are on the circumference or if one of the points is in the centre.
To help you plan your year 10 maths lesson on: Identifying which circle theorem to use, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Identifying which circle theorem to use, 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.∠AKC = 21°
∠AWK is subtended by the chord AK.
$$a$$° = °.
Q2.The image shows a circle, a tangent to the circle and three line segments forming a triangle inside the circle. The size of the angle labelled $$b$$° is °.
Q3.Find the size of angle $$c$$° (in degrees).
Q4.The size of angle $$d$$° is °.
Q5.The size of angle $$e$$° is ° .
Q6.Calculate the size of angle $$g$$° (in degrees).
Assessment exit quiz
6 Questions
Q1.Points X and Y are points where two separate tangents intersect the circle.
$$a$$° = °.
Q2.Points X and Y are points where two separate tangents intersect the circle.
Calculate the size of the angle labelled $$b$$°.
Q3.Points A and B are points where two separate tangents intersect the circle.
Calculate the size of the angle labelled $$c$$°.
Q4.Points A and B are points where two separate tangents intersect the circle.
$$d$$° = °.
Q5.The tangent shown intersects the circle at point T.
$$x$$° = °.
Q6.Point T is a point on the circumference where a tangent intersects the circle.
$$y$$° = °.