Each of the images below is a link to a step-by-step geogebra applet through which it is possible to move forwards and backwards in the construction, or watch how the construction is solved in a short animation. The blue “circular” points in some applets are movable.
These applets are gathered in this this geogebra book.
regular hexagon, given the large diagonal
regular hexagon, given the edge lenght
regular hexagon, given the short diagonal
regular hexagon, given the apothem
(the apothem is the distance between the center of a regular polygon and any of its sides; it is also the radius of its inscribed circle)