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

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Solution

Q.
If two tangents inclined at an angle of $60^{o}$ are drawn to a circle of radius 3cm, then the length of each tangent is equal to

1 $3 \sqrt{3} / 2 cm$

2 $3 cm$

3 $6 cm$

4 $3 \sqrt{3} cm$

Ans.
(4)

Angle between two tangents = $60 °$ (given)

$∴$ Tangents are equally inclined to each other

$∴$ $∠ O P A = ∠ O P B = 30 °$

and $∠ O A P = 90 °$

(Tangent is perpendicular to the radius)

In $∆ P A O,$ $\tan 30 ° = \frac{O A}{A P} \Rightarrow \frac{1}{\sqrt{3}} = \frac{3}{A P} \Rightarrow A P = 3 \sqrt{3}$

Hence, the length of each tangent is $3 \sqrt{3}$ cm

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