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O is the circumcentre of the triangle ABC and °BAC = 85°, °BCA = 75°, then the value of °OAC is
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- 55°
- 150°
- 20°
- 70°
- 55°
Correct Option: D
On the basis of question we draw a figure of a triangle ABC whose the circumcentre is O , 
Here , ∠BAC = 85°
∠BCA = 75°
∠ABC = 180° – 85° – 75° = 20°
We can say that angle subtended by an arc at the centre is twice to that subtended at any point on the circumference.
∴ 2∠ABC = ∠AOC
∴ ∠OAC = 40°
In ∆ OAC,
OA = OC = radii
∴ ∠OAC = ∠OCA
∴ 2∠OAC = 180° – 40° = 140°
| ⇒ ∠OAC = | = 70° | |
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