158.

Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60^o to each other.

Steps of construction:
(i) Take a point O on the plane of the paper and draw a circle of radius OA = 4 cm.
(ii) Produce OA to B such that OA = AB = 4 cm.
(iii) Draw a circle with centre at A and radius AB.
(iv) Suppose it cuts the circle drawn in step (i) at P and Q.
(v) Join BP and BQ to get the desired tangents.


Justification:
In ΔOAP, OA = OP = 4 cm ...(radii of the same circle)
Also, AP = 4 cm ….(Radius of the circle with centre A)

∴ ΔOAP is equilateral.
∠PAO = 60^o
∴ ∠BAP = 120^o
In ΔBAP, we have BA = AP and ∠ BAP = 120^o
 ∴∠ABP = ∠APB = 30^o
Similarly we can get ∠ABQ = 30^o
∴ ∠PBQ = 60^o