UPSC 2016 CDS II Math Paper

∠OQP = ∠ORP = 90°(Radius is perpendicular to the tangent at the point of contact)
Remember: If two tangents are drawn to a circle from an external point, then tangents are equally inclined to the segment joining the centre to that point.
∴ ∠OPQ = ∠OPR
=

∠QPR

2

=30°
In right ΔOPQ,
tan‌30°=

OQ

PQ

⇒

1

√3

=

3

PQ

⇒PQ=3√3cm
Therefore, the length of each tangent is 3√3cm