• Math

  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 10 months, 1 week ago 2 Members · 1 Reply
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  Krati

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  June 24, 2023 at 9:17 pm

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  The statement is false

  Explanation

  <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
  ∠OAB=∠OBA=60∘
  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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