Question

If the given figure, AOC is a diameter of the circle and arc AXB = $\frac{1}{2}$ arc BYC. Find ∠BOC.

Answer 1

We need to find

$$\begin{gathered} \mathrm{arc}AXB=\frac{1}{2}\mathrm{arc}BYC, \\ \angle AOB=\frac{1}{2}\angle BOC \\ \mathrm{Also}\angle AOB+\angle BOC=180° \\ \mathrm{Therefore},\frac{1}{2}\angle BOC+\angle BOC=180° \\ \Rightarrow \angle BOC=\frac{2}{3}\times 180°=120° \end{gathered}$$