Steps for Construction:

i)  draw a circle with centre O, with radius BC = 4.5 cm

ii) Draw arcs making an angle of 180º – 60º = 120º at O such that ∠AOB = 120º

iii) At A and B, draw two rays making an angle of 90º at each point which meet each other at point P, outside the circle.

iv) Then, AP and BP are the required tangents which make an angle of 60º with each other at P.