SSC CGL Tier II 25 Oct 2015 Paper 1

Question : 30 of 100

Marks: +1, -0

If O is the circumcentre of a triangle ABC lying inside the triangle, then ∠OBC + ∠BAC is equal to

90°
60°
110°
120°

Solution:

(1)

In ΔOBC ∵OB = OC
∴ΔOBC = ΔOCB
∴ ΔBOC = 180° – 2 ΔOBC
In ΔOBD,
ΔOBD = ΔOBC = 90° – ΔBOD
Angle subtended by an arc at the centre is twice to that subtended at the circumference.
∴ ∠BAC =

1/2

∠BOC
=

1/2

(180° – 2 ∠OBC)
= 90° – ∠OBC
∴ ∠BAC + ∠OBC = 90°

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