Proportion tutorial: triangle, hexagon, dodecagon, ...
Just about the first thing anyone does with a compass is make triangles and hexagons.

Start with a circle. Pick a point on the circle and make a circle around it of the same radius.

Use the points of intsrsection to add more circles of the same radius.

There will be 6 points thus produced; from them, one can make trangles and hexagons inside the circle.

By making a diameter that goes through a pair of secondary-circle intersections, and using the points where tha diameter cuts the original circle, one may add a second set of 6 points, and from those, make a dodecagon.

Please look at the source code of this page for more information.