Start by drawing a circle using a compass. Then, without changing the span of the compass mark the vertices of the hexagon on the circle.
See solution.
Practice makes perfect
We want to construct a regular hexagon inscribed in a circle. To do it, we will first draw a circle using a compass.
Next we will draw a point anywhere on the circle. This point will act as a starting point for our construction.
We are told that the side length of an inscribed regular hexagon is equal to the radius of the circumscribed circle.
Our compass already has the span equal to the radius. Thus,
without changing it we can draw the vertices of the hexagon on our circle. Let's place the compass point on point A and draw a small arc crossing the circle.
We can use the obtained point B to continue with our procedure. From here, we will place the compass point on point B and again draw a small arc crossing the circle.
We can continue to place the compass point on the intersection point and follow the same steps as with points A and B. We repeat the same procedure until we return to the starting point A.
Finally, using a straight edge we can connect the adjacent points with segments.
These segments have the same length, equal to the radius of a circumscribed circle. Thus, the constructed hexagon ABCDEF is a regular hexagon.
