MathematicsGiven that O is the center of the circle. Which of the following is the measure of ∠BAC?

Given that O is the center of the circle. Which of the following is the measure of ∠BAC?


  1. A
    85°
  2. B
    75°
  3. C
    65°
  4. D
    55° 

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    Solution:

    Given that,
    ∠AOB=80° and ∠AOC=110°
    The sum of all the angles at a given point is 360°.
    Then,
    ⇒∠AOB+∠AOC+∠BOC=360°
    ⇒80°+100°+∠BOC=360°
    ⇒190°+∠BOC=360°
    ⇒∠BOC=360°-190°
    ⇒∠BOC=170°
    The angle subtended by an arc at the center of the circle is double the angle subtended by it at any point on the circle.
    Thus,
    ⇒∠BOC=2∠BAC
    ⇒170°=2∠BAC
    ⇒∠BAC=170°2
    ⇒∠BAC=85°
    Hence, the measure of ∠BAC is 85°.
    Therefore, the correct option is 1.
     
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