Myths about teaching can hold you back
- Year 10•
- Higher
The tangents from an external point are equal in length
I can derive and use the theorem: the tangents from an external point are equal in length.
- Year 10•
- Higher
The tangents from an external point are equal in length
I can derive and use the theorem: the tangents from an external point are equal in length.
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
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 think that all circle theorems are about angles.
Circle theorems can be about angles or lengths in diagrams containing a circle.
To help you plan your year 10 maths lesson on: The tangents from an external point are equal in length, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: The tangents from an external point are equal in length, 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.The size of the angle labelled $$a$$° is °.

Q2.The size of the angle labelled $$b$$° is °.

Q3.∠ATC = 51°
∠ABT is subtended by the chord AT.
The size of the angle labelled $$e$$° is °.

Q4.∠PEF is subtended by the chord PF.
∠PFE is subtended by the chord PE.
Find ∠EPD (in degrees).

Q5.The size of angle $$c$$° is °.

Q6.Find the size of angle $$d$$° (in degrees).

Assessment exit quiz
6 Questions
Q1.A triangle is formed on the circle from a segment of a tangent, a radius and another line segment. The size of angle $$a$$° is °.

Q2.Points T and U are points where two separate tangents intersect the circle.
Find the size of angle $$b$$° (in degrees).

Q3.Points G and H are points where two separate tangents intersect the circle.
The size of angle $$c$$° is °.

Q4.Points Q and P are points where two separate tangents intersect the circle.
The size of the angle labelled $$d$$° is °.

Q5.Points J and K are points where two separate tangents intersect the circle.
The size of angle $$e$$° is °.

Q6.Points L and N are points where two separate tangents intersect the circle. ∠LMN = 118°.
$$g$$° = °.
