New
New
Year 10
Higher

The tangent at any point on a circle is perpendicular to the radius at that point

I can derive and use the theorem: the tangent at any point on a circle is perpendicular to the radius at that point.

New
New
Year 10
Higher

The tangent at any point on a circle is perpendicular to the radius at that point

I can derive and use the theorem: the tangent at any point on a circle is perpendicular to the radius at that point.

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Lesson details

Key learning points

  1. A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
  2. Theorems can be thought of as puzzles to solve, you are showing how to find a result
  3. 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.

Common misconception

Pupils may assume that tangents can be drawn in slightly different directions at the same point on a circle.

The tangent at a point on a circle can only be drawn in one possible direction. The tangent is always perpendicular to the radius at that point.

The lesson demonstrates how this circle theorem could be explored practically by using a circular geoboard and using dynamic geometry software. Pupils may wish to explore these further for themselves.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
The is a line which intersects the circle exactly once.
Correct Answer: tangent, tangent of a circle, circle tangent
Q2.
The size of the angle labelled $$x$$° is °.
An image in a quiz
Correct Answer: 26, 26°, 26 degrees
Q3.
MY = 8 cm, OZ = 13 cm, ZM = 12 cm, OM = 5 cm. Find the distance MX.
An image in a quiz
5 cm
8 cm
Correct answer: 12 cm
13 cm
Not enough information.
Q4.
The size of the angle labelled $$m$$° is ° (in degrees).
An image in a quiz
Correct Answer: 71, 71°, 71 degrees
Q5.
The size of the angle labelled $$a$$° is °.
An image in a quiz
Correct Answer: 46, 46°, 46 degrees
Q6.
The angle subtended from arc AB at the circumference of the circle is 11°. Find ∠BOA (in degrees).
An image in a quiz
5.5°
11°
Correct answer: 22°
79°
169°

6 Questions

Q1.
The size of the angle labelled $$x$$° on this 9-point geoboard is °.
An image in a quiz
Correct Answer: 80, 80°, 80 degrees, 80degrees
Q2.
Find ∠OAB on this 9-point geoboard (in degrees).
An image in a quiz
40°
Correct answer: 50°
80°
90°
Not enough information.
Q3.
Find ∠EFO on this 8-point geoboard (in degrees).
An image in a quiz
Correct Answer: 90, 90°, 90 degrees
Q4.
Find ∠DEF on this 8-point geoboard (in degrees).
An image in a quiz
Correct Answer: 45, 45°, 45 degrees, 45degrees
Q5.
Find the size of angle $$x$$° (in degrees).
An image in a quiz
Correct Answer: 13, 13°, 13 degrees
Q6.
Find the size of angle $$y$$° (in degrees).
An image in a quiz
Correct Answer: 79, 79°, 79 degrees