Question : If two tangents to a circle of radius 3 cm are inclined to each other at an angle of 60°, then the length of each tangent is:
Option 1: $\frac{3 \sqrt{3}}{4} \mathrm{~cm}$
Option 2: $3 \sqrt{3} \mathrm{~cm}$
Option 3: $3 \mathrm{~cm}$
Option 4: $6 \mathrm{~cm}$

Question

Question : If two tangents to a circle of radius 3 cm are inclined to each other at an angle of 60°, then the length of each tangent is:

Option 1: $\frac{3 \sqrt{3}}{4} \mathrm{~cm}$

Option 2: $3 \sqrt{3} \mathrm{~cm}$

Option 3: $3 \mathrm{~cm}$

Option 4: $6 \mathrm{~cm}$

Team Careers360 · Accepted Answer

Correct Answer: $3 \sqrt{3} \mathrm{~cm}$

Solution :
Let P be an external point, from where two tangents are drawn to the circle and the angle between them is 60°.
Join OA and OP.
OA = 3, is the radius of the circle.
Also, OP is the bisector of $\angle$P.
So, $\angle$APO = $\angle$CPO = 30°
Since tangents at any point of a circle are perpendicular to the radius through the point of contact.
So, OA $\perp$ AP
From $ riangle$OPA, We get,
$ an 30°=\frac{OA}{AP}$
⇒ $\frac{1}{\sqrt3}=\frac{3}{AP}$
$ herefore AP =3\sqrt3$
Tangents drawn from an external point are equal.
So, AP = CP = $3\sqrt3\ ext{cm}$
Hence, the correct answer is $3\sqrt3\ ext{cm}$.

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Question : If two tangents to a circle of radius 3 cm are inclined to each other at an angle of 60°, then the length of each tangent is:Option 1: 334 cmOption 2: 33 cmOption 3: 3 cmOption 4: 6 cm

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Question : If two tangents to a circle of radius 3 cm are inclined to each other at an angle of 60°, then the length of each tangent is:
Option 1: $\frac{3 \sqrt{3}}{4} cm$
Option 2: $3 \sqrt{3} cm$
Option 3: $3 cm$
Option 4: $6 cm$