Question

8
If two tangents are inclined at 60 degree
are drawn a circle of radius 3 cm then
find length of each tangent.
(1 Point)
54cm
116cm​

Answer 1

✬ Tangents = 3√3 cm ✬

Step-by-step explanation:

Given:

• Two tangents are inclined at 60°.
• Radius of circle is 3 cm.

To Find:

• What is the length of each tangent ?

Solution: Let in circle with centre O.

• AO = BO = 3 cm (radii)

• PA = PB (tangent)

• ∠APB = 60°

• ∠PAO = ∠PBO = 90° (tangent makes right angle at the point of contact)

Construction:

• Join PO such that its bisects ∠APB.

Now we have

• ∠APO = ∠BPO = 30°

Let's consider right angled ∆PBO we have

• OB = perpendicular

• PB = base

Applying tanθ there

$\implies{\rm }$ tanθ = P/B

$\implies{\rm }$ tan30° = 3/PB

$\implies{\rm }$ 1/√3 = 3/PB

$\implies{\rm }$ PB = 3√3

Hence, length of each tangents is 3√3 cm.

Answer 2

Answer:

✪ Given :-

• The two tangent are inclined at 60° and radius is 3 cm.

✪ To Find :-

• What is the length of each tangent.

✪ Solution :-

» Let, AB and AC are the two tangent are inclined at 60°.

» Radius is 3 cm.

↦ In right angle ∆AOB is,

⇒ tan30° = $\dfrac{DB}{AB}$

⇒ $\dfrac{1}{√3}$ = $\dfrac{3}{AB}$

➙ AB = 3$\sqrt{3}$

$\therefore$ The length of each tangent is $\boxed{\bold{\large{3\sqrt{3}}}}$

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