if you want to remove an article from website contact us from top.

    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

    Mohammed

    Guys, does anyone know the answer?

    get 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 from screen.

    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

    6 cm

    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

    Do you want to see answer or more ?
    Mohammed 11 day ago
    4

    Guys, does anyone know the answer?

    Click For Answer