This web page shows just how to construct (draw) a constant hexagoninscribed in a circle with a compass and straightedge or ruler. This is the biggest hexagon that will fit in the circle, with each vertextouching the circle. In a consistent hexagon, the side length is equal to the street from the facility to a vertex, so we use this fact to collection the compass come the suitable side length, then step around the circle noting off the vertices.

Printable step-by-step instructions

The above animation is available as a printable step-by-step accuse sheet, which can be used for do handoutsor once a computer system is no available.




You are watching: How to make a hexagon with a compass

Explanation that method

As deserve to be viewed in an interpretation of a Hexagon, every side of a regular hexagon is equal to the distance from the center to any vertex.This construction simply to adjust the compass broad to that radius, and also then steps that size off around the circleto create the six vertices the the hexagon.

Proof

The image listed below is the final illustration from the above animation, however with the vertices labelled.


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ArgumentReason1A,B,C,D,E,F all lie top top the circle OBy construction. 2AB = BC = CD = DE = EFThey were all drawn with the same compass width.From (2) we check out that five sides space equal in length, yet the last side FA was not drawn with the compasses.It to be the "left over" room as we stepped approximately the circle and also stopped in ~ F. For this reason we need to prove that is congruent with the other five sides.3OAB is an equilateral triangleAB was drawn with compass width set to OA, and OA = OB (both radii of the circle).4m∠AOB = 60°All inner angles the an it is intended triangle space 60°.5m∠AOF = 60°As in (4) m∠BOC, m∠COD, m∠DOE, m∠EOF are all &60deg;Since all the central angles include to 360°,m∠AOF = 360 - 5(60)6Triangle BOA, AOF space congruentSAS watch Test because that congruence, side-angle-side.7AF = ABCPCTC - corresponding Parts of Congruent Triangles room CongruentSo now we have all the piece to prove the construction8ABCDEF is a regular hexagon inscriptions in the given circleFrom (1), every vertices lie on the circleFrom (20), (7), all sides are the same lengthThe polygon has six sides.-Q.E.D


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Try that yourself

Other constructions pages top top this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and also Ellipses

Tangents to 2 circles (external) Tangents to two circles (internal)

Polygons

Non-Euclidean constructions

discover the center of a one with any right-angled object