Question

Larissa wants to inscribe a regular hexagon in a circle using only a compass and straightedge. She will construct a circle and finds its center. She will then perform the following steps.
Step 1: Plot a point on the circle to represent a vertex of the hexagon. Place the compass on this point and draw an arc to cut the circle. This represents the next vertex of the hexagon.
Step 2: Without adjusting the width of the compass, place the compass on this vertex and draw an arc to create the next vertex.
Step 3: Repeat the process to get a total of 6 vertices.
Step 4: Draw a line between successive pairs of vertices to form the regular hexagon.

What is the error in Larissa's construction?

A. She did not change the width of the compass when constructing the different vertices.
B. She did not set the width of the compass to the radius of the circle.
C. She did not set the width of the compass to the diameter of the circle.
D. She did not construct two perpendicular bisectors to construct two diameters of the circle.

Answer 1

Answer: option B. She did not set the width of the compass to the radius of the circle.

Explanation:

1) If she sets the compass to an arbitrary width to draw the arc to cut the circle, the point obtained will not be to the right distance from the first vertex.

2) All the adjacent vertices on a regular polygon have the same distance one from each other.

3) In the hexagon that distance is the same radius, which you can see becasue you can form six equilateral triangles inside the circle, whose side lengths are the radius.

4) So, she should set the width of the compass to the radius of the circle.