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Activity Discussion Math Circle

  • Circle

    Posted by Anagha on June 24, 2023 at 9:11 pm

    If a chord AB subtends an angle of 60° at the centre of a circle, then the angle between the tangents to the circle drawn from A and B is

    Krati replied 3 months ago 2 Members · 1 Reply
  • 1 Reply
  • Krati

    June 24, 2023 at 9:17 pm
    Not Helpful

    The statement is false


    <b style=”font-family: inherit; font-size: inherit; color: var(–bb-body-text-color); -webkit-text-size-adjust: 100%;”>Since a chord AB subtends an angle of 60∘at the centre of a circle

    i.e., ∠AOB=60∘
    As OA = OB = Radius of the circle
    The tangents at points A and B is drawn. Which intersect at C.
    We know. OA ⊥ AC and OB ⊥ BC
    ∴ ∠OAB=90∘,∠OBC=90∘
    ⇒ ∠OAB+∠BAC=90∘
    And ∠OBA+∠ABC=90∘
    ⇒ ∠ABC=90∘−60∘=30∘
    In △ABC∠BAC+∠CBA+∠ACB=180∘
    [Since sum of all interior angles of a triangle is 180∘]
    ⇒ ∠ACB=180∘−(30∘+30∘)=120∘

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