Diana is constructing a regular hexagon inscribed in a circle. She begins by drawing a line and labeling a point on the line as
point A. She uses her compass to construct a circle with point A as the center, labeling the points where the circle intersects the line as points B and C. Without changing the compass opening, she constructs a circle with point B as the center and then with point C as the center. What step should be her next step? Put the point of the compass on point B and the pencil point on point C. Using this compass width, put the compass point on A and draw another circle. Put the point of the compass on point B and the pencil point on point C. With the compass point still on B, draw two arcs that intersects the circle with center A. Draw and label the points where the circles with centers A and B intersect and where the circles with centers A and C intersect. Use a straightedge to join the four points where the circles intersect.
Draw and label the points where the circles with centers A and B intersect and where the circles with centers A and C intersect.
Step-by-step explanation:
Those four points of intersection, together with the points B and C are the 6 vertices of the hexagon. Diana can use her straightedge to join them to finish her inscribed hexagon.
