SATHEE: Quantitative Aptitude Ques 90

Quantitative Aptitude Ques 90

Question: A chord AB of a circle $ C _1 $ of radius $ (\sqrt{3}+1),cm $ touches a circle $ C _2 $ which is concentric to $ C _1. $ If the radius of $ C _2 $ is $ (\sqrt{3}-1),cm, $ then the length of AB is

Options:

A) $ 8\sqrt{3},cm $

B) $ 4\sqrt[4]{3},cm $

C) $ 4\sqrt{3},cm $

D) $ 2\sqrt[4]{3},cm $

Show Answer

Answer:

Correct Answer: B

Solution:

Let the chord AB of circle $ C _1 $ touches the circle $ C _2 $ at point M. Then, $ OA=\sqrt{3}+1 $ and $ OM=\sqrt{3}-1 $ Now, in right angled $ \Delta OAM, $ $ AM^{2}=OA^{2}-OM^{2} $ $ ={{(\sqrt{3}+1)}^{2}}-{{(\sqrt{3}-1)}^{2}} $

$ \Rightarrow $ $ AM^{2}=4\sqrt{3} $

$ \Rightarrow $ $ AM=2\sqrt[4]{3} $

$ \therefore $ $ AB=2AM=4\sqrt[4]{3} $

Quantitative Aptitude Ques 89

Quantitative Aptitude Ques 91

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