Final answer:
Constructing a regular hexagon, square, and equilateral triangle inscribed in a circle all begin with drawing a circle. The circle serves as a reference for creating the shapes with equal sides and correct angles using a compass.
Step-by-step explanation:
The construction of a regular hexagon, a square, and an equilateral triangle inscribed in a circle all have one common step: they each begin with the construction of a circle. Starting with a circle is essential, as it provides a reference from which to construct the equilateral sides of the triangle, the equal sides and right angles of the square, and the equal sides and angles of the hexagon with precision.
For each shape, one would typically use a compass to draw the circumscribing circle and then, with the same radius or a calculated length proportional to it, step off the necessary points on the circumference to create the vertices of the shape. For the triangle and the hexagon, this involves dividing the circumference into equal arcs, while for the square, special constructions are necessary to establish right angles.