The circumcentre of a triangle ABC is O. If ∠BAC = 85° and ∠BCA = 75°, then the value of ∠OAC is

A. 40°

B. 60°

C. 70°

D. 90°

Answer: Option C

Solution(By Examveda Team)

According to question,
Given:
∠BAC = 85°
∠BCA = 75°
∠OAC = ?

∠ABC + ∠BCA + ∠CAB = 180°
∠ABC = 20°
∴ ∠COA = 2 × ∠ABC
    ∠COA = 2 × 20 = 40°
In ΔAOC
We know OC = OA
∴ ∠OAC = ∠OCA
∴ ∠OAC + ∠OCA + ∠COA = 180°
2∠OAC = 180° - 40°
2∠OAC = 140°
∠OAC = 70°