∠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