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The circumcentre of a triangle ABC is O. If ∠BAC = 85° and ∠BCA = 75°, then the value of ∠OAC is
Answer & Solution
Correct Answer:
Option
C
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°
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°
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