AC is a diameter of the circle and arc AXB = 2 arc BYC. Find ∠BOC.


Answer:

60°

Step by Step Explanation:
  1. The ratio of the arc length to the circumference will be the same as the angle subtended by the arc/chord to the angle in a full circle (360°).
  2. Here, we know that arc AXB = 2arc BYC.
    This means ∠BOA = 2∠BOC.
  3. Also, AC is the diameter, and angle on a straight line is 180°. So, ∠BOA + ∠BOC = 180°.
    ⇒ 2∠BOC + ∠BOC = 180°
    ⇒ ∠BOC = 60°

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