Thinking like Euclid (Constructions)

David Wees, Rachel Morris, 07/09/2026

This is a sequence of geometric constructions, each designed as puzzles, where what students figure out how to do in one step can be used in future constructions. I recommend students using Geogebra first and then transferring their constructions (once they have them figured out) to paper using a compass and straightedge.


  • 1. #1 Draw a Circle
  • 2. #2 Given a Line Segment, Draw Another
  • 3. #3 Double the length of a line segment
  • 4. #4 Draw Two Circles
  • 5. #5 Given a Line Segment, Draw Another
  • 6. #6 Triple a Line Segment
  • 7. #7 Draw an Equilateral Triangle
  • 8. #8 Draw Three Circles
  • 9. #9 Two Circles That Touch Once
  • 10. #10 Find the Midpoint
  • 11. Challenge #11 Construct 2 Circles Inside a 3rd
  • 12. Challenge #12 Draw a Regular Hexagon
  • 13. Challenge #13 Construct a Square
  • 14. Challenge #14 Construct an Octagon

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#1 Draw a Circle

Given a line segment, draw a circle with its radius as the line segment.
– David Wees

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