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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Year 10

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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

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

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.

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.

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.

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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).