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Question -

In the AOC is a diameter of the circle and arc AXB = 1/2 arc BYC. Find ∠BOC.



Answer -

In the figure, AOC is diameter arc AxB =   arc BYC 1
∠AOB =  ∠BOC
⇒ ∠BOC = 2∠AOB
But ∠AOB + ∠BOC = 180°
⇒ ∠AOB + 2∠AOB = 180°
⇒ 3 ∠AOB = 180°
∴ ∠AOB == 60°
∴ ∠BOC = 2 x 60° = 120°

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