If two tangents inclined at an angle 60˚ are drawn to a circle of radius 3 cm, then find length of each tangent.

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# If two tangents inclined at an angle 60˚ are drawn to a circle of radius 3 cm, then find length of each tangent.

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## Dhiraj

Suppose O be the centre of the circle and PA and PB be the two tangents drawn from P to the circle so that ∠APB = 60°Join OP, OA and OB.In △OAP and △OBP,∠OAP = ∠OBP = 90° [radius is perpendicular to the tangent at the point of contact]OA = OB [radii]OP = OP [common]Therefore, △OAP ≅ △OBP [by RHS congruency]So, ∠OPA = ∠OPB = 30° [by cpct]In the right △OAP,tan 30° =^{OA}/_{AP}⇒^{1}/_{√3}=^{3}/_{AP}⇒AP= 3√3 cm = 3×1.732 cm = 5.196 cmSo,length of each tangent = 5.196 cm.