SSC CGL 16 Aug 2015 Shift 2 Paper

Question : 122 of 200

Marks: +1, -0

O is the circumcentre of ΔABC. If ∠BAC = 85°, ∠BCA = 75°, then ∠OAC is equal to :

60°
70°
50°
40°

Solution:

In Δ ABC,
∠ BAC = 85°
∠ BCA = 75°
∴ ∠ABC = 180° – 85° – 75° = 20°
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 DOAC,
∠OAC = ∠OCA (The angles at the base of an isosceles triangle are equal)
∠OAC + ∠OCA = 180° – 40° = 140°
∴ ∠OAC =

{140°}/2

= 70°

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