Question

In the given figure, if AOC is a diameter of the circle and AXB = $\frac{1}{2}$ are BYC, then ∠BOC = __________.

Answer 1

Given:
AOC is a diameter of circle
arc AXB = $\frac{1}{2}$ arc BYC
⇒ ∠BOA = $\frac{1}{2}$∠BOC ..(1)


Now, ∠BOA + ∠BOC = 180° (Angles on a straight line)
⇒ $\frac{1}{2}$∠BOC + ∠BOC = 180° (From (1))
⇒ $\frac{3}{2}$∠BOC = 180°
⇒ ∠BOC = $\frac{2}{3}\times$180°
⇒ ∠BOC = 120°


Hence, ∠BOC = 120°.