Question

If two tangents inclined at an angle 60 are drawn to a circle of radius 3cm then the length of each tangent is

Answer 1

we use trigonometry to find the length.

Tan 30° = 3 cm/Tangent
Tangent = 3 √3 cm  as tan 30° = 1/√3

Answer 2

Answer:

$\red { Length \: of \: each \: tangent }\green {= PA = PB = 3\sqrt{3}}$

Step-by-step explanation:

$Let \: PA \:and \: PB \: are \: two \: tangents$

$\angle APB = 60\degree \: ( given )$

$\angle OPA = \angle OPB = 30\degree$

$In \: \triangle OAP , \\ \angle OAP = 90\degree\: ( Tangent \: radius \: relation )$

$tan 30\degree = \frac{OA}{PA}$

$\implies \frac{1}{\sqrt{3}} = \frac{3}{PA}$

$\implies PA = 3\sqrt{3}$

Therefore.,

$\red { Length \: of \: each \: tangent }\green {= PA = PB = 3\sqrt{3}}$

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