(i) In Figure (1), is the center of the circle. If and find (ii) In figure (2), and are three points on the circle with center such that and Find

_{(i) Join OB.}

∠OAB = ∠OBA = 40°[Because OB = OA]

∠OCB = ∠OBC = 30°[Because OB = OC]

∠ABC = ∠OBA + ∠OBC

⇒ ∠ABC = 40°+ 30°

⇒ ∠ABC = 70°

∠AOC = 2 × ∠ABC

⇒ ∠AOC = 2 × ∠ABC

⇒ ∠AOC = 2 × 70°

⇒ ∠AOC = 140°

(ii)

∠BOC = 360° - (∠AOB + ∠AOC) [Sum of all angles at a point = 360°]

⇒ ∠BOC = 360° - (90° + 110°)

⇒ ∠BOC = 360° - 200°

⇒ ∠BOC = 160°

We know that ∠BOC = 2 × ∠BAC

⇒ ∠BAC = (1/2) × ∠BOC

⇒ ∠BAC = (1/2) × 160°

⇒ ∠BAC = 80°