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A regular hexagon in a circle

Values

Construct a regular hexagon ABCDEF with sides of 3 cm, in a circle.

Construct a regular hexagon ABCDEF with sides of 2.5 cm, in a circle.

Construct a regular hexagon ABCDEF with sides of 3.5 cm, in a circle.

Construct a regular hexagon ABCDEF with sides of 4 cm, in a circle.

O012345cm

1. With O as the center and radius 3 cm, draw a circle.

2. Mark a point A on the circle and draw the radius OA. With A as the center and the same radius, 3 cm, cut the circle at B.

3. With B as the center and the same radius, cut the circle at C. Go on round: D, E and F.

4. Join AB, BC, CD, DE, EF and FA: ABCDEF is a regular hexagon. The last cut lands back on A.

1. With O as the center and radius 2.5 cm, draw a circle.

2. Mark a point A on the circle and draw the radius OA. With A as the center and the same radius, 2.5 cm, cut the circle at B.

3. With B as the center and the same radius, cut the circle at C. Go on round: D, E and F.

4. Join AB, BC, CD, DE, EF and FA: ABCDEF is a regular hexagon. The last cut lands back on A.

1. With O as the center and radius 3.5 cm, draw a circle.

2. Mark a point A on the circle and draw the radius OA. With A as the center and the same radius, 3.5 cm, cut the circle at B.

3. With B as the center and the same radius, cut the circle at C. Go on round: D, E and F.

4. Join AB, BC, CD, DE, EF and FA: ABCDEF is a regular hexagon. The last cut lands back on A.

1. With O as the center and radius 4 cm, draw a circle.

2. Mark a point A on the circle and draw the radius OA. With A as the center and the same radius, 4 cm, cut the circle at B.

3. With B as the center and the same radius, cut the circle at C. Go on round: D, E and F.

4. Join AB, BC, CD, DE, EF and FA: ABCDEF is a regular hexagon. The last cut lands back on A.

Step 1 of 4
Why it works

Each cut is the radius from the last point, so O and two neighbouring points make an equilateral triangle, with 60° at O. Six of them go exactly round the 360° at the center: the six sides are equal to the radius, and each angle of the hexagon is 60° + 60° = 120°.