Steps of Construction :
(i) Take a point O on the plane of the paper and draw a circle of radius OA = 5 cm.
(ii) Produce OA to B such that OA = AB = 5 cm.
(iii) Taking A as the centre draw a circle of radius AO = AB = 5 cm.
(iv) It cuts the circle at P and Q.
(v) Join BP and BQ to get the desired tangents.
Justification :
In AOAP, we have
OA = OP = 5 cm (= Radius)
Also, AP = 5 cm (Radii of circle)
∴ ΔOAP is equilateral.
⇒ ∠PAO = 60°
⇒ ∠BAP = 120°
In ΔBAP, we have
BA = AP and ∠BAP = 120°
∴ ∠ABP = ∠APB = 30°
⇒ ∠PBQ = 60°