How to construct a regular octagon

Let's consider a given segment equal to the length of a side of the required octagon. You want to build a regular octagon. The first step construct an isosceles triangle on a given segment using the line segment as base. To do this, first construct a square with side equal to the segment, swipe it diagonally. Now construct bisectors of the angles at the diagonals (in the figure the bisectors are indicated in blue), at the intersection of the bisectors of the images of the vertices of an isosceles triangle whose sides equal the radius of the circle circumscribed about a regular octagon.

Construct a circle with center at the vertex of the triangle. The radius of the circle is equal to side of triangle. Now spread the compass to the distance equal to the value of the specified segment. Mark this distance on the circumference, starting from either end of the segment. Connect all the points obtained in the octagon.

If the circle in which must be inscribed octagon, the build will be even easier. Construct two mutually perpendicular axial line passing through the center of the circle. At the intersection of the axial and circumference get four vertices of the octagon of the future. It remains to divide the distance between these points on the arc of a circle in half to obtain four more vertices.