Question

which construction requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments? a regular hexagon inscribed in a circle an equilateral triangle inscribed in a circle a square inscribed in a circle a similar circle inscribed in a circle

Explanation:

1. For a regular hexagon inscribed in a circle: We start from a point on the circle, use the radius to mark off equal - length arcs around the circle. We don't need to connect the endpoints of a diameter in the described way.
2. For an equilateral triangle inscribed in a circle: We first draw a diameter. Then, using the endpoints of the diameter as centers and the radius of the circle as the radius of the arcs, we draw arcs that intersect the circle. Connecting the endpoints of the diameter and the intersection points of the arcs with the circle in order gives an equilateral triangle.
3. For a square inscribed in a circle: We use perpendicular diameters, not the construction described in the question.
4. A similar circle inscribed in a circle is not constructed in this way.

Answer:

B. an equilateral triangle inscribed in a circle