Steps of construction :
(i) Draw BC = 3.5 cm.
(ii) At B draw BE such that EBC = 67.1/2˚. From BE cut off BA = 5 cm.
(iii) Join AC. Then ABC is the required triangle.
(iv) Produce EB to F.
(v) At B draw BG such that ∠EBG = 90˚.
(vi) Draw perpendicular bisector of BC to cut BG at O.
(vii) With O as centre and OB as radius draw a circle. This is the required circle to touch AB at B and pass through C.