Question

What are the steps used to construct a hexagon inscribed in a circle using a straightedge and a compass?

1) an isosceles triangle ABC is drawn with point D on side AC
2) an altitude is drawn from point B to point D
3) point D lies on side AC
4) point B is equidistant from points A and C

Answer 1

The correct steps to construct a hexagon inscribed in a circle involve creating six equal arcs with a compass that intersect the circle, using one vertex as the starting point, and then connecting the vertices with a straightedge.

Step-by-step explanation:

The task of constructing a hexagon inscribed in a circle using a straightedge and compass involves several steps, which are not directly related to the initially provided student question details. To properly construct an inscribed hexagon, follow this process:

1. Begin with the given circle and a point on the circle that will be one vertex of the hexagon.
2. Place the compass point on this vertex, extend the compass to the center of the circle, and draw an arc to intersect the circle, creating a second vertex of the hexagon.
3. Without changing the compass width, repeat this process around the circle to create the remaining vertices of the hexagon.
4. Connect adjacent vertices using the straightedge to form the hexagon.

This correct method utilizes the geometric properties of a hexagon, specifically that its side lengths are equal to the radius of the circumscribed circle. Neither the string, pins, and pencil method for drawing an ellipse, nor the other geometric properties outlined in the provided information, are relevant to constructing a regular hexagon.