Question

which construction uses the compass for only one step in addition to drawing the circle itself?
an equilateral triangle inscribed in a circle
a square inscribed in a circle
a regular hexagon inscribed in a circle
a diameter of a circle

Explanation:

• For an inscribed equilateral triangle: Requires multiple compass arcs to mark vertices after drawing the circle.
• For an inscribed square: Needs compass work to find perpendicular bisectors/vertices beyond the initial circle.
• For an inscribed regular hexagon: Uses repeated compass arcs (same radius as the circle) to mark 6 vertices, multiple steps.
• For a circle diameter: After drawing the circle, place the compass on one point on the circle, set it to a length greater than the radius, draw two arcs above and below the circle; then repeat from the opposite side to find the diameter line. This is only one additional compass step set beyond drawing the circle.

Answer:

a diameter of a circle