AC is a diameter of the circle and arc AXB = 2 arc BYC. Find ∠BOC.
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Step by Step Explanation:
- 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°).
- Here, we know that arc AXB = 2arc BYC.
This means ∠BOA = 2∠BOC.
- Also, AC is the diameter, and angle on a straight line is 180°. So, ∠BOA + ∠BOC = 180°.
⇒ 2∠BOC + ∠BOC = 180°
⇒ ∠BOC = 60°