Final answer:
To construct a hexagon inscribed in a circle using a straightedge and compass, first draw a circle. Then draw line segments from the center to different points on the circumference. Use these segments to create arcs on the circle and find points of intersection. Connect the intersection points to form the hexagon.
Step-by-step explanation:
Draw a circle using a compass.
Use a straightedge to draw a line segment from the center of the circle to any point on its circumference.
Place the compass on the point where the line segment intersects the circle and adjust the compass width to the distance between the center and the point of intersection.
This is the radius of the circle.
With the compass centered at the circle's center, draw arcs on the circumference of the circle that intersect the line segment.
Repeat steps 3 and 4 to create two more points of intersection.
Connect the points of intersection to form a hexagon inscribed in the circle.