Question

o is circumcentre of a ∆ABC
prove OBA + ACB
90°​

Answer 1

Answer:

O is the centre of circumscribed circle.

OB = OC = radii

⇒ ∠OBC = ∠OCB = x

∴ x + x + ∠BOC = 180° (Angle sum property of △OBC)

2x + ∠BOC = 180°

∠BOC = 180° - 2x

Also, ∠BOC = 2∠BAC

180° - 2x = 2∠BAC

⇒ 90 - x = ∠BAC

∴ ∠BAC + ∠OBC = (90° - x) + x

∠BAC + ∠OBC = 90°