Draw a circle circumscribing a regular hexagon with side = 5 cm.

(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.

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.

Using a ruler and compasses only :

(i) Construct a triangle ABC with the following data :

AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.

(ii) In same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.

(iii) Measure ∠BCP.