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SSC CGL 2022 PYQ — Question 22

SSC CGL Tier II - Quant - 29 Jan 2022 • Quantitative Aptitude • Q22

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O is a point in the interior of △ABC such that OA = 12 cm, OC = 9 cm, ∠AOB = ∠BOC = ∠COA and ∠ABC = 60º. What is the length (in cm) of OB?

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Correct answer: C

Explanation

 The correct answer is option 3 i.e. 6√3

∠AOB = ∠BOC = ∠COA = a (let).

3a = 360

a = 120

∠AOB = ∠BOC = ∠COA = 120°

If one let ∠ABO = θ\theta then , ∠OBC = (60 - θ\theta)

Then ∠OCB = θ\theta and ∠BAO = (60 - θ\theta).

So one can say that △AOB is similar to the △BOC,

OB/OA = OC/OB

OB2 = OA × OC

OB = 6√3.