Question

if two tangents inclined at an angle 60 are drawn to a circle of radius 4 cm then length of each tangent​

Answer 1

Answer:

Lengthofeachtangent=PA=PB=3

3

Step-by-step explanation:

Let \: PA \:and \: PB \: are \: two \: tangentsLetPAandPBaretwotangents

\angle APB = 60\degree \: ( given )∠APB=60°(given)

\angle OPA = \angle OPB = 30\degree∠OPA=∠OPB=30°

\begin{lgathered}In \: \triangle OAP , \\ \angle OAP = 90\degree\: ( Tangent \: radius \: relation )\end{lgathered}

In△OAP,

∠OAP=90°(Tangentradiusrelation)

tan 30\degree = \frac{OA}{PA}tan30°=

PA

OA

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

3

1

=

PA

3

\implies PA = 3\sqrt{3}⟹PA=3

3

Therefore.,

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

3

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