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:

1. Equilateral triangle inscribed in a circle: After drawing the circle, we need multiple compass - steps to find the vertices of the equilateral triangle. We use the compass to mark off arcs of equal length around the circle to get the vertices.
2. Square inscribed in a circle: After drawing the circle, we need to use the compass to construct perpendicular diameters (more than one compass - step) to find the vertices of the square.
3. Regular hexagon inscribed in a circle: After drawing the circle, with the radius of the circle set on the compass, we can step around the circle to mark the vertices of the hexagon. We only need to use the compass one more time (after drawing the circle) to mark off the six equal - length arcs around the circle.
4. Diameter of a circle: We can use a straight - edge to draw a diameter through the center of the circle. If we want to use a compass, we may need to use it more than once to find the center and then draw a line through the center.

Answer:

C. a regular hexagon inscribed in a circle