Home » Aptitude » Plane Geometry » Question
  1. O is the circumcentre of ∆ ABC. If ∠BAC = 85°, ∠BCA = 75°, then ∠OAC is equal to :
    1. 60°
    2. 70°
    3. 50°
    4. 40°
Correct Option: B

According to question , we draw a figure of triangle ABC circumscribes a circle with centre O

In ∆ ABC,
Given , ∠ BAC = 85° , ∠ BCA = 75°
∴ ∠ABC + ∠ BAC + ∠ BCA = 180°
∴ ∠ABC = 180° – 85° – 75° = 20°
We can say that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
∴ ∠AOC = ∠ABC = 40°
∴ OA = OC = radii
In ∆ OAC, ∠OAC = ∠OCA
(The angles at the base of an isosceles triangle are equal)
∠OAC + ∠OCA = 180° – 40° = 140°

∴ ∠OAC =
140°
= 70°
2



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