O is the circumcentre of ∆ABC, given ∠BAC = 85° and

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O is the circumcentre of ∆ABC, given ∠BAC = 85° and ∠BCA = 55°, find ∠OAC.

1. 40°
2. 50°
3. 60°
4. 80°

Correct Option: B

According to question , we draw a figure of triangle ABC whose the circumcentre is O

Given , ∠BAC = 85°
∴ ∠BOC = 2 × 85° = 170°
∠BCA = 55°
∴ ∠AOB = 2 × 55° = 110°
We know that , ∠AOC + ∠BOC + ∠AOB = 360°
∴ ∠AOC = 360° – 170° – 110° = 360° – 280° = 80°

∴ ∠OAC = ∠OCA =	1	(180° - 80°)
	2

∠OAC =	1	× 100 = 50°
	2