Question

A, B and C are three points on a circle such that the angles subtended by the chord AB and AC at the centre O are 110° and 130o, respectively. Then the value of ∠BAC is:

• A. 65°
• B. 75°
• C. 60°
• D. 70°

Answer 1

Answer:

C. 60°

∠AOB = 110° and ∠ AOC = 130

In ΔOAB

∠AOB + ∠OBA + ∠BAO = 180

2∠OAB = 180° - 110°

∠OAB = 35°

Now in Δ OAC

∠OAC +∠ACO + ∠COA = 180°

2∠OAC = 180° - 130°

∠OAC = 25°

Hence ∠BAC = ∠OAB + ∠OAC = 35° + 25° = 60°