SSC CGL 30 Aug 2015 Paper

Question : 123 of 200

Marks: +1, -0

O is the circumcentre of the triangle ABC and ∠BAC = 85°, ∠BCA = 75°, then the value of ∠OAC is

55°
150°
20°
70°

Solution:

∠BAC = 85°
∠BCA = 75°
∠ABC = 180° – 85° – 75°
= 20°
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 ΔOAC,
OA = OC = radii
∴ ∠OAC = ∠OCA
∴ 2∠OAC = 180° – 40° = 140°
⇒ ∠OAC =

{140°}/2

= 70°

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