The correct answer is:

B. only a regular hexagon or an equilateral triangle inscribed in a circle

Explanation:

1. By setting the compass width to the radius of the circle and marking six points on the circle's boundary, Jordan has effectively divided the circle into six equal arcs. These points are spaced exactly one radius apart around the circle.

2. Connecting these six points with a straightedge will create a regular hexagon inscribed within the circle. This is a standard construction for an inscribed hexagon.

3. Additionally, Jordan can form an equilateral triangle by connecting every other point on the circle (three points separated by two arcs each). This configuration will also lie symmetrically within the circle.

4. However, constructing a square inscribed within a circle would require dividing the circle into four equal parts, which this six-point division does not achieve. Therefore, a square cannot be constructed with the given setup.

Thus, Jordan can construct only a regular hexagon or an equilateral triangle using the six equally spaced points.

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Would you like further details on the geometry behind this construction or have any questions?

Here are five questions that expand upon this concept:

1. How does setting the compass width to the radius ensure six equal divisions on a circle?
2. Why can't a square be constructed using the six-point division on the circle?
3. What is the relationship between the radius of a circle and the side length of the inscribed hexagon?
4. How does connecting every other point on a hexagon create an equilateral triangle?
5. What other regular polygons can be inscribed in a circle using compass and straightedge constructions?

Tip: A regular hexagon can always be constructed inside a circle by stepping around with the circle's radius, as each side length of the hexagon matches the radius.