Question

which step do the constructions of a regular hexagon, a square, and an equilateral triangle inscribed in a circle all have in common? draw segments connecting all of the points of intersection on the circle. draw a line segment connecting the two points where the arc intersects the circle. construct a diameter using the center of the circle and the points where the small arc intersects the line segment. construct an arc using an endpoint of the diameter and the center of the circle.

Explanation:

When inscribing a regular hexagon, square, or equilateral triangle in a circle, a common first - step is to construct an arc using an endpoint of the diameter and the center of the circle. This helps in finding key points on the circle for further construction of the polygon. For a hexagon, the radius of the circle is used to mark off equal arcs around the circle. For a square and equilateral triangle, similar arc - construction steps based on the circle's properties are part of the initial process.

Answer:

Construct an arc using an endpoint of the diameter and the center of the circle.