Mathematics
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 angle bisectors of A and B which intersect each other at O.
Draw OL ⊥ AB.
With centre O and radius OL, draw a circle which touches the sides of hexagon. This is the required incircle of hexagon ABCDEF.
Related Questions
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.
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 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.
Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.