Mathematics [3 marks sum]

 
Steps of Construction:
i) Draw a regular hexagon ABCDEF with each side equal to 5 cm and each interior angle 120º.
ii) Join its diagonals AD, BE and CF intersecting each other at O.
iii) With centre as O and radius OA, draw a circle which will pass through the vertices A, B, C, D, E and F.
This is the required circumcircle.

 
i) O is called the incentre of the incircle of ΔABC.
ii) OR and OQ are the radii of the incircle and OR = OQ.
iii) OC is the bisector of angle C
∴ ∠ACO=∠BCO