Steps of construction :
1. Draw AC = 8 cm.
2. Draw perpendicular bisector of AC = cut it at I.
3. Cut IB = 6/2 = 3 cm and ID = 3 cm and join ABCD. Then ABCD is the required rhombus.
4. Now from I draw a perpendicular to BC to meet it at L.
5. With I as centre and IL as radius, draw a circle which is the required circle. Its radius = IL = 2.4 cm.