Steps to inscribe a regular hexagon in a circle:

Step 1: Draw a circle. Mark point A on the circle.
Step 2: Draw an arc centered at point A, with the same radius as the circle. Mark the point where the arc intersects the circle.
Step 3: From that point of intersection, draw another arc with the same radius. Mark the point where that arc intersects the circle.
Step 4: Repeat until you have made 6 arcs.
Step 5: Connect the 6 points to form a regular hexagon.

How does the construction ensure that the sides of the hexagon are the same length as the radius?

A hexagon is inscribed in a circle. Arcs are at each point on the circle. Point A is on the circle.
CLEAR CHECK

All the vertices are the same distance from the center.


The arcs used to locate the points have the same radius as the circle.


A ruler can be used to verify that the sides are the same as the radius.


This construction will not create sides equal to the radius.