Question

Lena 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.

What step should be her next step?

Without changing the compass opening, construct a circle with point C as the center.

Draw a line through point A and either of the two points where the circles intersect.

Draw a line through the points where the two circles intersect.

Increasing the compass opening, construct a circle with point C as the center.

Answer 1

Answer:
Without changing the compass opening, construct a circle with point C as the center.

If you do this procedure you realize that you have found 6 points equally distributed over the original circumference. Of course they are at the same distance of the point A, which is the center of the first circle.

So, those 6 points equally distributed over the original circle define the hexagone.