Euclide's Elements - BOOK IV - Proposition 15
In this activity you are going to use the following tools. Make sure you know how to use each tool before you begin with the actual construction of the hexagon: Circle with center through point - Intersect two objects - Polygon - Angle - Show / hide object - Move.
Construction process
1. Draw a circle with center A through point B
2. Construct another circle with center B through point A
3. Intersect the two circles in order to get the vertices C and D.
4. Construct a new circle with center C through point A.
5. Intersect the new circle with the first one in order to get vertex E.
6. Construct a new circle with center D through point A.
7. Intersect the new circle with the first one in order to get vertex F.
8. Construct a new circle with center E through point A.
9. Intersect the new circle with the first one in order to get vertex G.
10. Draw hexagon FGECBD.
11. Create the angles of the hexagon.
12. Perform the drag test to check if your construction is correct.
Hint: You might want to have a look at the file http://www.comathsnet.it/geogebra/second_task.html if you are not sure about the construction process. Below you can find its View/Construction Protocol.
Challenge: Try to find an explanation for this construction process.
Hint: Which radius do the circles have and why?