Draw the pair of tangents to …

In order to draw the pair of tangents, we follow the following steps.

Steps of construction
STEP I Take a point O on the plane of the paper and draw a circle of radius OA = 5 cm.
STEP II Produce OA to B such that OA = AB = 5 cm.

STEP III Taking A as the centre draw a circle of radius AO = AB = 5 cm. Suppose it cuts the circle drawn in step I at P and Q.
STEP IV Join BP and BQ to get the desired tangents.
Justification: In OAP, we have
OA = OP = 5 cm (= Radius)
Also, AP = 5 cm (= Radius of circle with centre A)
{tex}\therefore{/tex} {tex}\Delta O A P{/tex} is equilateral. {tex}\Rightarrow \angle P A O = 60 ^ { \circ } \Rightarrow \angle B A P = 120 ^ { \circ }{/tex} 
In {tex}\Delta B A P{/tex}, we have
BA = AP and {tex}\angle B A P{/tex} = 120°
{tex}\angle A B P = \angle A P B = 30 ^ { \circ }{/tex}
{tex}\Rightarrow \quad \angle P B Q = 60 ^ { \circ }{/tex}