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Tangent to a circle

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

A tangent (Tangente) touches the circle in exactly one point. It is perpendicular to the radius to that point.
📄 Open worksheet (PDF, German)

The video

In the video we tell apart a line that misses the circle, a secant and a tangent, and construct the tangent at a point \(B\) with the set square.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:20 Tangent and radius
  3. 0:36 Construction
  4. 0:58 Careful, mistake!
  5. 1:20 Try it yourself

The most important points

Line and circle

Passant (Passante): no common point. Tangent: exactly one point, the point of contact \(B\). Secant (Sekante): two points of intersection.

Passant, secant and tangent on the same circle.
Passant, secant and tangent on the same circle.

Tangent and radius

The radius \(MB\) is perpendicular to the tangent. So the tangent is at distance \(r\) from the centre.

Construction: draw the radius \(MB\). Put the set square with its zero point on \(B\) and its middle line on \(MB\). Draw the tangent along the edge.

The tangent at B, at a right angle to the radius.
The tangent at \(B\), at a right angle to the radius.

Careful: drawn by eye (here \(70^\circ\)), the line cuts the circle a second time: a secant.

Slanted to the radius: a second point of intersection.
Slanted to the radius: a second point of intersection.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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The worksheet – Page 4
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Show the worksheet solutions
The worksheet – Page 5
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Try it yourself

Task

Draw a circle with \(r = 2{,}5\,\text{cm}\) and a point \(B\) on the circle. Construct the tangent at \(B\). How far is it from \(M\)?

Show solution

Radius \(MB\), then the perpendicular at \(B\). Distance \(= r = 2{,}5\,\text{cm}\).

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: tangent to a circle (Tangente): passant, secant, construction. Give me five short tasks, one after the other. Always wait for my answer. Then tell me if it is right and explain briefly why. Use simple German sentences.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.