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# if two tangents inclined at an angle of 60ᵒ are drawn to a circle of radius 3cm, then the length of each tangent is equal to

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### Mohammed

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## If two tangents inclined at an angle 60^∘ are drawn to a circle of radius 3 cm, then length of each tangent is equal to:

Click here👆to get an answer to your question ✍️ If two tangents inclined at an angle 60^∘ are drawn to a circle of radius 3 cm, then length of each tangent is equal to: If two tangents inclined at an angle 60

Question ∘

are drawn to a circle of radius 3 cm, then length of each tangent is equal to:

A

2 3 ​ 3 ​ cm

B

C

## 3 cm

D3

3 ​ Medium Open in App

स्रोत : www.toppr.com

## If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to a. 3√3/2 cm, b. 6 cm, c. 3 cm, d. 3√3 cm

If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to a. 3√3/2 cm, b. 6 cm, c. 3 cm, d. 3√3 cm - If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to 3√3 cm If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to

a. 3√3/2 cm b. 6 cm c. 3 cm d. 3√3 cm

Solution:

Given, two tangents are drawn to a circle of radius 3 cm, inclined at an angle of 60°

We have to find the length of each tangent. From the figure,

Let PA and PC be the tangents drawn to a circle

PA and PC inclined at 60°

So, ∠APC = 60°

We know that the tangents through an external point to a circle are equal.

So, PA = PC

In triangle OAP and triangle OCP,

PA = PC

OA = OC = radius of circle

OP = OP = common side

By SSS criterion, triangles OAP and OCP are similar,

We know that the radius of a circle is perpendicular to the tangent at the point of contact.

So, ∠OAP = ∠OCP = 90°

Since OA = OC = radius

∠OAP = ∠OCP ∠APC = ∠OAP + ∠OCP So, 2∠OAP = 60° ∠OAP = 60°/2 ∠OAP = 30° In triangle OAP,

OAP is a right triangle with A at right angle.

tan 30° = OA/AP

By trigonometric ratio of angles,

tan 30° = 1/√3 So, 1/√3 = 3/AP AP = 3√3 cm

We know, AP = CP = 3√3 cm

Therefore, the length of each tangent is 3√3 cm.

✦ Try This: If two tangents inclined at an angle 60° are drawn to a circle of radius 5 cm, then length of each tangent is equal to☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10NCERT Exemplar Class 10 Maths Exercise 9.1 Problem 9

## If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to a. 3√3/2 cm, b. 6 cm, c. 3 cm, d. 3√3 cm

Summary:

If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to 3√3 cm

☛ Related Questions:

In Fig. 9.8, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR . . . .

In Fig. 9.9, BOA is a diameter of a circle and the tangent at a point P meets BA extended at T. If ∠ . . . .

In Fig. 9.10, PQL and PRM are tangents to the circle with centre O at the points Q and R, respective . . . .

स्रोत : www.cuemath.com

## Question 9 If two tangents inclined at an angle 60∘ are drawn to a circle of radius 3 cm, then the length of each tangent isA 3/2√3 cmB 6 cmC 3 cmD 3 √3 cm

Question 9 If two tangents inclined at an angle 60∘ are drawn to a circle of radius 3 cm, then the length of each tangent isA 3/2√3 cmB 6 cmC 3 cmD 3 √3 cm Home

Question 9 If two tangents inclined at an angle 60∘ are drawn to a circle of radius 3 cm, then the length of each tangent isA 3/2√3 cmB 6 cmC 3 cmD 3 √3 cm

Question

If two tangents inclined at an angle

60 ∘

are drawn to a circle of radius

3 c m ,

then the length of each tangent is

(A) 3 2 √ 3 c m (B) 6 c m (C) 3 c m (D) 3 √ 3 c m Open in App Solution Let P

be an external point and a pair of tangents is drawn from point P and angle between these two tangents is

60 ∘ Radius of the circle

= 3 c m Join OA and OP

Also, OP is a bisector line of

∠ APC ∴ ∠ A P O = ∠ C P O = 30 ∘ O A ⊥ A P

Also, tangents at any point of a circle is perpendicular to the radius through the point of contact.

In right angled Δ O A P , we have tan 30 ∘ = O A A P = 3 A P ⇒ 1 √ 3 = 3 A P ⇒ A P = 3 √ 3 c m A P = C P = 3 √ 3 c m

[Tangents drawn from an external point are equal]

Hence, the length of each tangent is

3 √ 3 c m . Suggest Corrections 32 SIMILAR QUESTIONS

Q. If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm, then the length of each tangent is (a) 3 cm (b) 6 cm (c) 332cm (d) 33cm

Q. Question 9

If two tangents inclined at an angle

60 ∘

are drawn to a circle of radius 3 cm, then the length of each tangent is

(A) 3 2 √ 3 cm (B) 6 cm (C) 3 cm (D) 3 √ 3 cm

Q.

### If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then the length of each tangent is equal to?

Q. Construct a pair of tangents to a circle of radius

3 c m

, which are inclined to each other at an angle of

60 ∘

स्रोत : byjus.com

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Mohammed 11 day ago

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