Question

Draw a regular hexagon of side 3.6 cm. Construct a circle inscribing the regular hexagon.

Answer 1

Steps of Construction:

• Draw a line segment OA = 3.6 cm. This will be the radius of the inscribing circle.
• With centre O and radius 3.6 cm, draw a circle. This circle will be used to construct the regular hexagon.
• Mark point A on the circle. 
• With A as the centre and radius 3.6 cm, mark point B on the circumference.
• With B as the centre and the same radius (3.6 cm), mark point C on the circle.
• Continue this process from the points
  C → D
  D → E
  E → F and finally F → A
• So that AB = BC = CD = DE = EF = FA = 3.6 cm.
• Join the points in order: A–B, B–C, C–D, D–E, E–F, and F–A to get the required regular hexagon ABCDEF.
• The circle already drawn with radius 3.6 cm is the inscribed circle,
  since a regular hexagon satisfies: Side = Radius of the incircle (when the hexagon is inscribed in a circle).