The bisectors of angles A and B of a scalene triangle ABC meet at O.

(i) What is the point O called ?

(ii) OR and OQ are perpendiculars drawn to AB and CA respectively. What is the relation between OR and OQ ?

(iii) What is relation between angle ACO and angle BCO ?

(i) Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5 cm.

(ii) Find its incenter and mark it I.

(iii) With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle.

Draw an inscribing circle of regular hexagon of side 5.8 cm.

Construct a triangle ABC in which base BC = 5.5 cm, AB = 6 cm and ∠ABC = 120°.

(i) Construct a circle circumscribing the triangle ABC.

(ii) Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.