SATHEE: Quantitative Aptitude Ques 1470

Quantitative Aptitude Ques 1470

Question: Two chords of lengths a m and b m subtend angles $ 60{}^\circ $ and $ 90{}^\circ $ at the centre of the circle, respectively. Which of the following is true?

Options:

A) $ b=\sqrt{2}a $

B) $ a=\sqrt{2}b $

C) $ a=2b $

D) $ b=2a $

Show Answer

Answer:

Correct Answer: A

Solution:

In $ \Delta AOB, $ $ AO=BO=r $ [radius of circle] $ b^{2}=r^{2}+r^{2} $ $ b=\sqrt{2r^{2}} $

$ \Rightarrow $ $ b=\sqrt{2},r $ (i) In $ \Delta COD, $
$ \angle COD=60{}^\circ $ Then, $ \angle OCD=\angle ODC $ $ =180{}^\circ -\angle COD $ $ =180{}^\circ -60{}^\circ $ $ =120{}^\circ $ Also, $ \angle OCD=\angle ODC= $ Angle opposite to equal sides.

$ \therefore $ $ \angle OCD=\angle ODC=60{}^\circ $ So, $ \Delta COD $ is equilateral and $ r=a $ … (ii) From Eqs. (i) and (ii), we get $ b=\sqrt{2},a $

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Quantitative Aptitude Ques 1470

Question: Two chords of lengths a m and b m subtend angles $ 60{}^\circ $ and $ 90{}^\circ $ at the centre of the circle, respectively. Which of the following is true?

Options:

Answer:

Solution:

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