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Drawing circles

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

You learn about the centre, the radius and the diameter and draw circles with a pair of compasses.
📄 Open worksheet (PDF, German)

The video

In the video the compasses are set with the ruler of the set square. At the top right you see the radius that is set.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:11 The circle
  3. 0:47 The compasses
  4. 1:19 Setting the compasses
  5. 1:51 Drawing a circle
  6. 2:26 Radius and diameter
  7. 2:50 Careful, mistake!
  8. 3:05 Try it yourself

The most important points

The circle

The centre (der Mittelpunkt) \(M\) is in the middle. Every point of the circumference (die Kreislinie) is the same distance from \(M\). The radius \(r\) goes from \(M\) to the circumference. The diameter (der Durchmesser) \(d\) goes through \(M\): \(d = 2 \cdot r\), \(r = d : 2\).

Radius r = 4 cm, diameter d = 8 cm.
Radius \(r = 4\) cm, diameter \(d = 8\) cm.

Drawing a circle

Make the needle point (die Zirkelspitze) and the pencil lead (die Bleistiftmine) the same length. Set the compasses with the ruler: needle point on 0, pencil lead on the radius (turn the adjusting screw, die Rändelschraube). Mark the centre with a cross, push the needle in, turn only by the handle (der Griff), tilt a little.

The compasses are set to 4 cm.
The compasses are set to 4 cm.

Don't hold the legs: otherwise the radius changes and the circle does not close.

Mistake: the compasses opened, the circle does not close.
Mistake: the compasses opened, the circle does not close.

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

a) \(r = 6\) cm, how big is \(d\)? b) \(d = 7\) cm, to how many cm do you set the compasses?

Show solution

a) \(d = 2 \cdot 6 \text{ cm} = 12\) cm b) \(r = 7 \text{ cm} : 2 = 3.5\) cm

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: circles (Mittelpunkt, Radius, Durchmesser, d = 2 · r) and drawing circles with a pair of compasses. 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.