Quantitative Aptitude Ques 384

Question: Two circles touch each other internally. Their radii are 2 cm and 3 cm. The biggest chord of the greater circle which is outside the inner circle is of length

Options:

A) $ 2\sqrt{2},cm $

B) $ 3\sqrt{2},cm $

C) $ 2\sqrt{3},cm $

D) $ 4\sqrt{2},cm $

Show Answer

Answer:

Correct Answer: D

Solution:

  • Let O and O’ be the centres of greater and smaller circles, respectively.

$ \therefore $ $ OM=O’M=OO’=2-1=1 $ In $ \Delta AOM, $ $ AM^{2}=OA^{2}-OM^{2} $ $ =9-1=8 $

$ \Rightarrow $ $ AM=2\sqrt{2} $

$ \therefore $ Length of biggest chord, $ AB=2\cdot AM=4\sqrt{2} $

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