UPSC 2013 CDS 2 Math Paper

Height of the balloon, OB = h
Tangents are equally inclined to the line joining the centre of the circle and the external point from where the tangents are drawn.∴∠OAP=∠OAQ=‌‌

60∘

2

=30∘
Also ∠OPA=90°
Remember:
Radius is perpendicular to the tangent at the point of contact
In ΔOAp
sin‌30°=

1

2

=

r

OA

⇒OA=2r
In ΔOAB
sin‌60°=

√3

2

=

h

OA

⇒h=

√3

2

×2r=√3r   (OA=2r)