Question

If two tangents are inclined at 60˚ are drawn to a circle of radius 3cm then

find length of each tangent​

Answer 1

Answer:

Let PA and PB be the two tangents to a circle with centre O and radius 3

∴∠APO=∠BPO

=

2

1

​

×∠APB

=

2

1

​

×60

0

=30

0

Also, OA⊥AP and OB⊥BP

In a right angled triangle OAP,

tan30

0

=

PA

3

​

⇒

3

​

1

​

=

PA

3

​

⇒PA=3

3

​

cm

⇒PA=PB=3

3

​

cm

Step-by-step explanation:

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Answer 2

Answer:

The angle ABO is 30 degrees since the line from the center of the circle bisects the angle between two tangents from a point. Hence AB =4√3 cm. So, the lengths of tangents = AB = BC = 4√3cm. Hence the correct option is B.