Question

Draw a regular hexagon of side 4.2 cm. Construct a circle inscribing the regular hexagon.

Answer 1

Steps of Construction:

1. Draw a line segment OA = 4.2 cm. This will be the radius of the circle used to construct the regular hexagon.
2. With centre O and radius 4.2 cm, draw a circle. This circle will be used to construct the regular hexagon.
3. Mark point A on the circle.
4. With A as centre and radius 4.2 cm, cut an arc on the circumference to obtain point B.
5. With B as the centre and the same radius (4.2 cm), cut another arc to get point C.
6. Continue this process from the points:
   

   C → D,
   D → E,
   E → F,
   and finally F → A, so that all the sides: AB = BC = CD = DE = EF = FA = 4.2 cm are equal.

7. Join the points in order: A–B, B–C, C–D, D–E, E–F, and F–A to obtain the required regular hexagon ABCDEF.

8. To construct the inscribed circle, draw the angle bisectors of any two adjacent angles of the hexagon. Their intersection gives the centre O of the incircle.
   Then draw a perpendicular from O to any side of the hexagon.
   The length of this perpendicular is the radius of the incircle.
   With this radius and centre O, draw the inscribed circle.