Steps of construction :
(i) Take BC = 20 cm.
(ii) Make ABC = 45˚ and with centre B, cut the arc BA = 9 cm.
(iii) Join AC, so ABC is the required triangle.
(iv) With A as centre and radius = 25 cm, draw a circle. It will pass through D.
(v) Draw DE and AB, which cuts BC at E.
(vi) Draw the angle bisector of BED which cut BD at O.
(vii) Taking radius = OD draw a circle which touches the first circle at D and also touches the line BC at F.
(viii) This is the required circle. The radius OD = 2.7 cm