Inscribe a regular polygon

The question

Inscribe a regular hexagon.

How it works.

compass+straightedge

Step 1→Keep the compass set to the circle's radius for the whole construction

Step 2→Put the point anywhere on the circle and mark an arc across it

Step 3→Move the point to that mark and repeat, all the way around — you get six marks

Step 4→Join the six marks in order

arcs=the evidence

01
Inscribe a regular hexagon. Use only a compass and a straightedge — no measuring.
02
1. Keep the compass set to the circle's radius for the whole construction. Keep the compass at the circle's radius the whole time.
03
2. Put the point anywhere on the circle and mark an arc across it. A chord as long as the radius makes an equilateral triangle with the center, so it cuts off 60°.
04
3. Move the point to that mark and repeat, all the way around — you get six marks. Six lots of 60° is a full turn, so the sixth step lands back where you started. If it does not, the compass slipped.
05
4. Join the six marks in order. Joining every mark gives a regular hexagon; joining every other one gives an equilateral triangle.
06
Leave every arc showing — they show how the figure was made.