Mathematics
Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.
Constructions
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Answer
We know that each angle in a regular hexagon = 120°.
Draw a line segment AB = 4 cm.
At A and B draw rays making an angle of 120° each and cut off AF = BC = 4 cm.
At F and C, draw rays making angle of 120° each and cut off EF = CD = 4 cm.
Join ED. Hence, ABCDEF is the required hexagon.
Draw the perpendicular bisector of AB and BC. Let these bisectors meet at the point O.
With O as center and radius equal to OA or OB draw a circle which passes through the vertices of the hexagon. This is the required circumcircle of hexagon ABCDEF.
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Related Questions
Using ruler and compasses only, construct a triangle ABC in which BC = 4 cm, ∠ACB = 45° and the perpendicular from A on BC is 2.5 cm. Draw the circumcircle of triangle ABC and measure its radius.
Draw a regular hexagon of side 4 cm and construct its incircle.
Construct a △ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.
Using ruler and compasses only, construct a △ABC such that BC = 5 cm, AB = 6.5 cm and ∠ABC = 120°.
(i) Construct a circumcircle of △ABC.
(ii) Construct a cyclic quadrilateral ABCD such that D is equidistant from AB and BC.